report im-agimb

Transcrição

report im-agimb

INDEX
Welcome ............................................................................................................................... 1
Brief Description .................................................................................................................... 3
Areas of Activities and Coordinators ...................................................................................... 5
Reports of Activities - Summaries .......................................................................................... 9
Reports of Activities
Mathematical Instruction and Olympiads .............................................................................. 19
Weather Prediction and Climate .......................................................................................... 23
Control Theory .................................................................................................................... 28
Optimization and Electrical Energy ...................................................................................... 35
Computer Graphics ............................................................................................................. 46
Mathematical Modeling of Biological Systems and of Linguistics .......................................... 53
Differential Geometry .......................................................................................................... 61
Algebra and Algebraic Geometry ......................................................................................... 70
Dynamical Systems ............................................................................................................. 77
Topology and Singularities .................................................................................................. 94
Combinatorics and Algorithms ............................................................................................. 107
Operator Algebras and Harmonic Analyses ......................................................................... 114
Partial Differential Equations ............................................................................................... 116
Mathematical Economy and Finances ................................................................................. 126
Probability ........................................................................................................................... 129
Petroleum Sciences ............................................................................................................ 132
Cooperation with Latin America ............................................................................................134
Emerging Centers ............................................................................................................... 137
Federal University of Alagoas .............................................................................................. 141
Federal University of Amazonas .......................................................................................... 139
Federal University of Bahia ................................................................................................. 143
Federal University of Campina Grande ................................................................................ 146
Federal University of Espírito Santo .................................................................................... 149
Federal University of Goiás ................................................................................................. 152
Federal University of Maranhão ........................................................................................... 156
Federal University of Pará ................................................................................................... 158
Federal University of Paraíba .............................................................................................. 162
Federal University of Paraná ............................................................................................... 166
Federal University of Piauí .................................................................................................. 170
Virtual Emerging Center ...................................................................................................... 172
Post-Doctoral Fellowships ................................................................................................... 175
Scientific Initiation Fellowships ............................................................................................ 176
1
Rio de Janeiro, 6 th October 2004.
Dear Colleagues,
We have the pleasure to inform you about the activities of the Millennium Institute - Global
and Integrated Advancement of Mathematics in Brazil and Contribution to the Region that
have been taking place in the last three years or so (since January, 2002). Its activities
have a comprehensive character aiming at the global advancement of Mathematics and
Applications in Brazil. It should also contribute to the enhancement of Mathematics in Latin
America.
The Millennium Institute brings together in a comprehensive and yet coherent way many of
the most active research groups in Brazilian institutions, such as the National Institute for
Pure and Applied Mathematics - IMPA, National Laboratory for Scientific Computation LNCC, Center for Weather Forecast and Climatic Studies and National Institute for Space
Research - CPTEC/INPE, Institute of Mathematics and Statistics - IME and Institute of
Astronomy and Geophysics - IAG of the State University of São Paulo - USP, State
University of Campinas - UNICAMP, State University of São Paulo at São Carlos USP/São Carlos, Institute of Mathematics, Institute of Biophysics and COPPE of the
Federal University of Rio de Janeiro - UFRJ, Catholic University of Rio de Janeiro – PUC –
Rio, University of Brasília - UnB and Federal Universities of Minas Gerais - UFMG, Rio
Grande do Sul - UFRGS, Santa Catarina - UFSC, Pernambuco - UFPe, Ceará - UFC,
Fluminense - UFF and São Carlos - UFSCar.
The activities that have been planned focus on an intense collaboration of the research
groups involved in this Virtual Institute of Excellence. The project sets a new step in the
development of Brazilian Mathematics as a whole, in a much broader basis, emphasizing
applications and the integration of Mathematics with other areas of Science and to some
extent the productive sector. Also, the Institute adds a vigorous effort to improve
mathematical instruction, diffusion of mathematics and the search for talents.
In the front of applications are the areas of Modeling of Biological Systems, Climate and
Weather Prediction, Petroleum, Mathematical Economics and Finances and efforts in
Optimization/Eletric Energy, with some predictable technological impacts as well as to the
environment. Also of much social impact is the improvement of mathematical instruction.
Another main objective is to give support to the Emerging Research Centers, especially in
the Northern, Northeastern and Center Western regions of Brazil such as the Federal
Universities of Amazonas, Pará, Maranhão, Paraíba, Alagoas, Bahia, Espírito Santo,
Goiás, Campina Grande, Piauí and the Virtual Emerging Center formed by the Federal
Universities of Viçosa, Ouro Preto, São João del Rei and Uberlândia and, in addition, the
Federal University of Paraná. Much emphasis is given to the cooperation with Latin
America, both to foster joint research projects and the organization of conferences and
workshops, as well as to contribute to the upbringing of the high level human resources.
The figure that follows provides a global view of the areas of activities.
Thank you all for your enthusiastic cooperation that has allowed us to achieve the goals
set for our Virtual Institute of Excellence.
Best regards,
Jacob Palis
1
2
A Brief Description
Brazilian Mathematics has now a solid international prestige, being qualified by the
International Mathematical Union in the same group of countries as Australia, China,
Hungary, Holland, India, Poland and Spain based on its scientific activity. The Virtual
Institute of Excellence - the Millennium Science Institute "A Global Integrated
Advancement of the Brazilian Mathematics and a Contribution to the Development of
Mathematics in Latin America" is a major vehicle to providing a new dimension to this
fundamental area for our scientific and technological development. It's certainly mobilizing
most of the national leadership in this domain to achieve a new level of excellency through
the following goals:
•
•
•
•
•
•
The number of centers of competence in mathematics is being substantially amplified
in the different regions of the country;
The research activity has been more comprehensive, encompassing applications and
computational modeling concerning, for instance, extraction of oil, climate and weather
prediction, modeling of biological systems and others;
Special attention is being given to the nurturing of Ph.D. students, aiming at amplifying
the number and diversifying the areas, keeping high standards. The same applies to
Post-Doctoral programs, resulting in a bigger number of active researchers in the area;
Directly support is given to Emerging Centers, preferably in the Northern, Northeastern
and Center Western regions of Brazil;
A pilot program for improving mathematical teaching at the secondary and
fundamental levels is being implemented. Also one for improving the diffusion of
mathematics and the search for talents through the National Olympiads. In the latter,
especial attention is given to increase the participation of Brazil in International
Olympiads and to the Regional Olympiads in Brazil;
The scientific cooperation among Brazilian researchers as well as with those of the
main Latin America centers and at the Northern Hemisphere has being increasing
substantially. In particular, several Fields Medallists are taking part in this project, that
is, they are part of such a Virtual Institute of Excellence.
There are research groups in the following universities and scientific centers:
IMPA - http://www.impa.br
INPE-CPTEC - http://www.inpe.br/english
LNCC - http://www.lncc.br
PUC-Rio - http://www.puc-rio.br
University of Brasília - http://www.unb.br
University of Campinas - http://www.unicamp.br
IME - http://www.ime.usp.br and IAG - http://www.master.iag.usp.br of the State
University of São Paulo at São Paulo
State University of São Paulo at São Carlos - http://www.sc.usp.br
Federal University of Santa Catarina - http://www.ufsc.br
Federal University of Pernambuco - http://www.ufpe.br
Federal University of São Carlos – http://www.ufscar.br
Federal University of Minas Gerais - http://www.ufmg.br
Federal University Fluminense - http://www.uff.br
Federal University of Rio de Janeiro - http://www.ufrj.br
Federal University of Ceará - http://www.ufc.br
Federal University of Rio Grande do Sul - http://www.ufrgs.br
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Support to Emerging Centers:
Federal University of Alagoas - http://www.ufal.br
Federal University of Amazonas - http://www.fua.br
Federal University of Bahia - http://www.ufba.br
Federal University of Campina Grande - http://www.ufcg.edu.br
Federal University of Espírito Santo - http://www.ufes.br
Federal University of Goiás - http://www.ufg.br
Federal University of Maranhão - http://www.ufma.br
Federal University of Pará - http://www.ufpa.br
Federal University of Paraíba - http://www.ufpb.br
Federal University of Paraná- http://www.ufpr.br
Federal University of Piauí - http://www.ufpi.br
and the newly added Virtual Emerging Center formed by:
Federal University of Viçosa - http://www.ufv.br
Federal University of Ouro Preto - http://www.ufop.br
Federal University of São João del Rei - http://www.ufsj.edu.br
Federal University of Uberlândia - http://www.ufu.br
The following figure indicates the main activities and the organizational structure of this
Millennium Institute:
Activities
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Research Areas, Instruction and Olympiads, Cooperation, Emerging Centers
Activities and Coordinators
Mathematical Instruction and Olympiads
§ E. L. Lima - IMPA
§ C. G. Moreira - IMPA
Weather Prediction and Climate
§ A. Nachbin - IMPA
§ C. Nobre - INPE/CPTEC
§ P. L. Silva Dias - IAG/USP
Control Theory
§ M. Fragoso - LNCC
Optimization and Electrical Energy
§ A. Iusem - IMPA
§ J. M. Martinez - UNICAMP
§ C. Tomei - PUC-Rio
Computer Graphics
§ L. Velho - IMPA
§ P. C. Carvalho - IMPA
§ R. Beauclair - IMPA
§ R. Feijóo - LNCC
Mathematical Modeling of Biological Systems and of Linguistics
§ J. Koiller - LNCC
§ J. Zubelli - IMPA
§ W. Zin - UFRJ
§ C. Galves - UNICAMP
Differential Geometry
§ L. Barbosa - UFCE
§ M. Dajczer - IMPA
§ J. Ripoll - UFRS
Algebra and Algebraic Geometry
§ A. Hefez - UFF
Dynamical Systems
§ A. Lopes - UFRS
§ M. Vianna - IMPA
§ M. Soares - UFMG
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Topology and Singularities
§ P. Schweitzer - PUC-Rio
§ M. A. Ruas - USP/São Carlos
Combinatorics and Algorithms
§ Y. Kohayakawa - IME/USP
Operator Algebras and Harmonic Analysis
§ R. Exel - UFRS
Partial Differential Equations
§ J. Hounie - UFSCarlos
§ H. Frid - IMPA
§ O. Lopes - UNICAMP
Mathematical Economy and Finances
§ C. Landim - IMPA
§ A. Araújo - IMPA
Probability
§ M. E. Vares - CBPF
Petroleum Sciences
§ M. Tygel - UNICAMP
§ A. Loula - LNCC
§ D. Marchesin - IMPA
Cooperation with Latin America
§ C. Camacho - IMPA
Emerging Centers
Federal University of Alagoas
§ H. Alencar
Federal University of Amazonas
§ R. Tribuzy
Federal University of Bahia
§ E. Vergasta
Federal University of Campina Grande
§ A. Souza
Federal University of Espírito Santo
§ F. Guimarães
§ V. Bayer
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Federal University of Goiás
§ R. Garcia
Federal University of Maranhão
§ N. Muniz
Federal University of Pará
§ J. Corrêa
Federal University of Paraíba – Campus I, João Pessoa
§ J. M. Bezerra do Ó
Federal University of Paraná
§ J. Yuan
Federal University of Piauí
§ J. Xavier
Virtual Emerging Center
Federal Universities of Viçosa, Ouro Preto, Uberlândia and São João del Rei
§ O. Miyagaki
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Millennium Institute
Global and Integrated Advancement of Mathematics in Brazil – IM-AGIMB
Report of Activities - Summaries
Areas
Mathematical Instruction
The Program for Improvement of High School Teachers of Mathematics is an activity of
the Institute of the Millenium, with the support of IMPA and RNP (National Research and
Education Network). The Program started in 2002 and happens twice a year, in January
and July (school vacations period). The first session, held in January 2002, included 6
Brazilian states. Little by little, this number increased so that the last one, held in July
2004, counted with 20 states, some of them with more than one city participating. The
attendance included over 1400 teachers. The interest shown by the participants is
remarkable, with an increasing number of them taking part at the successive events,
totaling about five thousand teachers since the beginning of the project. For the next
meeting, planned to be held in January 2005, we expect more states to take part. Each
stage of the program lasts one week (5 days) with daily activities during 8 hours. The team
of instructors consists of E. L. Lima (coordinator), P. C. P. Carvalho, E. Wagner and A. C.
Morgado. We believe that this initiative of the Millenium Institute is of great importance for
the improvement of the Mathematics teaching, causing upgrading and homogenization all
over the country. It is also to be noted that the publications it generates, as well as its
presence at the Internet add an important aspect of permanence to its effect. We are
certain of the importance of the project and we hope to be able to count with funds to
increase the reach and expansion of this program, attaining a larger and larger number of
participants. For this purpose, it is essential to continue to count on the invaluable
contribution the Millenium Institute, IMPA and RNP, as well as the enthusiasm and the
never failing collaboration of J. Palis, a friend and believer in promoting good level
mathematical instruction since the first day.
Olympiads
Olympiads in mathematics are under way in approximately 85 countries, and they occur on
national, regional and international scales. If properly structured, Olympiads may serve as
major instruments for promoting sciences to young students. They are vehicles for
improvement of science teachers’ skills, and they aid in the detection of young scientific
talents. To achieve these three goals, the Olympiads should be large-scale events in each
country, at several grade levels and in three different stages at each level. The first test is
very friendly to students and their teachers, with many winners and simple prizes. The
second stage involves those who performed well in the first stage. Finally, a third stage
determines the best talents, who then compete internationally and are awarded fellowships
for further science training. This is precisely the structure of the Brazilian National
Mathematics Olympiads promoted by the Brazilian Mathematical Society and the National
Council for Scientific and Technological Development – CNPq. IM-AGIMB has been a new
partner in this important activity with two goals: to promote regional or state Olympiads
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within Brazil and to expand the Brazilian participation in international competitions,
specially the International Mathematics Competition for University Students. IM-AGIMG´s
contribution led to a participation of more than 130,000 students in the Regional
Olympiads in different States of Brazil, as well as to excellent performances at the
International Mathematics Competition for University Students, including the award of a
golden medal in 2004.
The contributions of the Millenium Institute IM-AGIMB have been invaluable, regarding the
global and integrated advancement of Mathematics within related areas such as Weather
Prediction and Climate. There has never been such an agile advancement as was
observed in the past 30 months. Most important, the interchange of efforts, technology and
human resources has been reciprocal. The specific reports clearly indicate this fact, which
has been observed in the connection between Meteorology and Mathematics, as well as
between Theoretical Physics and Mathematics. In this last case flexibility and agile
decision making allowed several activities to materialize over a small time span. In
particular the exchange of researchers, an international workshop (an initiative of the
Institute of Theoretical Physics IFT/UNESP; partially in response to IM-AGIMB efforts)
which generated a contact with the Consortium of the Americas for Interdisciplinary
Sciences (University of New Mexico) and a proposal for a summer course (2005) at IMPA
by a physicist of IFT/UNESP. Meteorology is also well integrated with Mathematics.
Among several efforts described in the corresponding reports, the IM-AGIMB activities had
an impact on a doctoral thesis of the Brazilian Center for Weather Forecasting and Climate
Studies (CPTEC/INPE). They also promoted a (future) visit to the USA by a PhD student in
Meteorology, of the Institute of Astronomy, Geophysics and Atmospheric Sciences
(IAG/USP). This student will visit the Courant Institute and also the Mathematics
Department of the University of Wisconsin at Madison (one semester each institute). In
Climate Studies important conceptual advances were reached in the period. Of particular
interest was the theoretical discovery of multiple stable equilibria in the biome-climate
coupled system for Tropical South America. The interaction of the vegetated surface and
the atmosphere through the turbulent fluxes of momentum, heat, water vapor and other
substances is highly nonlinear. The CPTEC Atmospheric General Circulation Model
(AGCM), was coupled to a biome model recently developed at CPTEC, was used to
numerically search for multiple biome-climate stable equilibria. Two stable states were
found when the numerical calculations were started with contrasting conditions. In
Weather Prediction, the group continues to focus improving the efficiency of numerical
methods used in simulation models for the atmospheric climate system, as well as on
theoretical aspects for the atmospheric flow. In particular those connected with nonlinear
effects and also originated from perturbation of the atmospheric flow. Another activity in
this area is Waves in Heterogeneous Media, theme of interest in Mathematics (differential
equations in multiple scales, with highly oscillatory coefficients), in Theoretical Physics and
Meteorology. A recent PhD graduate in this field obtained a post doctoral position at the
University of California at Irvine (USA). Several research articles were published in the
different subareas, and several PhD students graduated from the different subgroups. IMAGIMB is planning several workshops/events in the near future, in particular a School in
Environmental Modeling. The success of interdisciplinary IM-AGIMB activities has been
clearly observed in an international workshop on Ensemble Forecasting (CPTEC 2002).
Consolidating the IM-AGIMB’s goals is of fundamental importance, together with its ease
to plan activities (such as events/workshops, domestic and international exchange of
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researchers, among others), for the further development of Brazilian Mathematics as well
as of other areas in Science and Technology.
Control Theory
For the past thirty months, the 8 members of the control group of IM-AGIMB carried out a
host of activities which includes the publication of 34 papers in top journals, 2 books to be
published, the conclusion of 10 PhD and 6 MSc theses and coordinate the activities of 4
pos-doc visitors. In addition, the group had an intense program of interaction with many
universities in Brazil and abroad (7 in South America, 6 in Europe, 2 in USA, 1 in Australia,
1 in Israel and 1 in Singapura). Furthermore, an international conference (CIMPA School
and Workshop on Geometric Non-Linear Control from 14-23 July 2003,
http://www.ime.unicamp.br/~cntrl03/) has been organized. IM-AGIMB program has not
only given a decisive contribution to the success of the control group via supporting their
activities, but has also introduced a very important element that is the possibility of
planning activities such as research work involving colleagues from different institutions
and conferences, which sometimes requires some period of time, before they take place.
An important feature of IM-AGIMB, among others, is that it allows the planning of all key
activities in a flexible and agile manner, which are critical issues for their successes.
Finally, hoping that this very successful program (IM-AGIMB) continues for the next three
years, the control group plans as its general main priorities for the near future: (1) to
consolidate the prestige in the international community, via highly relevant scientific
contributions, participation in conferences and training of PhDs students; (2) to organize
conferences, workshops, etc., (3) to carry out a special visiting program for top
researchers in important strategic research topics; and (4) To bring together other local
research groups, involving in particular those with a more application-oriented motivation.
Optimization and Electrical Energy
Continuous optimization in Brazil began a process of steady development in the eighties,
almost exclusively concentrated in the Rio de Janeiro and São Paulo areas. During the
last two decades these research groups became strong and well connected to the
international community, while several smaller groups bloomed in all regions of the
Country. By the turn of the century there was good diversity in research lines, including
theory, algorithms and applications, but the community was scattered in the Country with
no appropriate discussion forum. Cohesion in this community was then sought with the
organization of Brazilian workshops on continuous optimization, which began as small and
exclusively national events. The last two workshops, in 2002 and 2004, mark a new phase
in the area: they were jointly organized by the Millennium Institute and local committees,
becoming now well attended international meetings. The Millennium Institute has also
promoted post-doctoral programs and regional meetings, thus playing an important role in
the global progress of Optimization in Brazil. Another key aspect of the importance of the
Millenium Institute for the recent sharp development of Optimization in Brazil was its
encompassing support to the Centers in Development, that includes the Federal University
of Paraná, as well as the Federal Universities of Piauí in the North-Eastern and Goias in
the Center-West, regions were scientific development is much needed. Remarkably, good
level meetings are planned for the Centers in Paraná and Goiás in the near future.
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Computer Graphics and Vision
In the area of Computer Graphics and Vision, relevant research has been developed in the
following topics, as described in the detailed report: Multiresolution Models; 3D
Photography Immersive Visualization, Video and Multimedia. There have also been
developments related to the following applications: Medical Imaging, GIS (Geographic
Information Systems) and Digital Television. The Millennium Institute, IM-AGIMB, has
decisively contributed to the advancement of Computer Graphics and Vision in Brazil
during the last 30 months. In this regard, the Institute promoted the planning and
organization of a great number of activities. Among those initiatives, we can mention:
scientific visits (travel grants for the researchers Jonathan Schewchuk and Nina Amenta);
research incentive (post-doctoral scholarship for A. Peixoto); organization of scientific
events (Workshop on Geometric Processing and Applications; creation of emerging
centers (Group Graphic Computation of Federal University of Alagoas - UFAL). Thus, it is
important to emphasize the key role played by the IM-AGIMB giving more flexibility to
multi-institutional projects and creating synergy among the groups in the area.
Since its beginning, the IM - AGIMB institute has been contributing in an invaluable way to
a much-needed interdisciplinary effort by supporting biomathematics workshops, lectures,
and courses. This comes in the direction of mitigating the lack we have in Brazil of
scientists with a solid common background in the mathematical sciences and in the
biophysical sciences. The full impact of such contribution will be consolidated only in the
next few years, when young researchers and students that participated in the different
events start to develop research in those areas. It should also be pointed out that the
research activities of the IM-AGIMB influenced directly the development of several fields.
To cite a few, we point out: Advances in mathematical techniques for respiratory function
monitoring, by W. Zin and collaborators. Modeling of the circulatory system, by R.Feijóo
and collaborators. Fractals in biology, by L. Bevilacqua. Scaling limit techniques of kinetic
models (Boltzmann equation), which started to be used in a very effective way in the joint
work developed by F. Chalub, P. Markowich, and B. Perthame to tackel chemotaxis
problems. Effective algorithms based on tridimensional tomographic methods to tackle
transmission microscopy problems in the macro-molecule imaging, which was developed
by J. P. Zubelli jointly with the group of G. T. Herman (CUNY). New techniques of
epidemiology and virus dynamics, especially those using quasi-species equations and
evolutionary biology (Hofbauer, May, Nowak, Sigmund). The study of flagellated microorganism mobility by means of geometrical mechanics techniques, in the work developed
by J. Koiller jointly with K. Ehlers, G. Huber, e G. A. Araujo. The study of symmetry in the
genetic code and finite groups and preservation of symmetries in the evolution of the
genetic code.
IM-AGIMB has been also instrumental in the development of research in stochastic
modeling in linguistics and the nurturing of human resources. The main three topics of
research were: 1) probabilistic methodology developed in order to study linguistic chains,
with several relevant contributions by A. Galves, Fernandez, Gabrielli, Guiol, Collet,
Duarte, Garcia, Cuesta-Alberto, Fraiman, Svarc; 2) linguistic-probabilistic modeling with
important contributions by C.Galves, A.Galves, Duarte, Peixoto, Mandel, Sândalo,
Abaurre, Abadi, Garcia; 3) modeling the interface syntax/phonology using optimality
theory, with relevant contributions by Abaurre, C. Galves, A. Galves, Mandel, Sândalo.
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The contribution of the IM-AGIMB to the progress of mathematical research and to the
training new researchers was of fundamental importance by promoting the planning and
organization of high level activities. In fact, without the support of IM-AGIMB, these
activities would never have the importance they actually represented for the development
of the area of Differential Geometry in the country. Its existence means a tremendous
effort to maintain an international high level standard of research in Brazil. IM-AGIMB
made it possible to give a strong support to the mobility of the geometers all over the
country, promoting their participation (many of them coming from distant places) in the
different events promoted by IM-AGIMB (the two National Schools of Differential Geometry
in Goiâna and São Paulo, the Workshops of Maceió and Canela, the Summer Schools of
Fortaleza), as well as the presence of invited researchers in universities and research
institutes. Moreover, with the support of IM-AGIMB, it became possible to bring to Brazil
outstanding foreign mathematicians who contributed decisively for the success of the
events. These researchers also visited several universities and research institutes. IMAGIMB made possible the insertion in the geometers’ research web of new researchers
who finished recently their Ph.Ds. in high level national or foreign institutions, giving a
fundamental contribution to new partnerships in research works. These partnerships are
producing new topics of research, as well as the use of new techniques in problems
traditionally investigated by Brazilian geometers. It is also fundamental to point out that this
intense mobility promoted by IM-AGIMB propitiated a more frequent contact among
researchers and young promising mathematical students, stimulating them to pursue their
Ph.Ds, especially in Differential Geometry. As an immediate result of the strong and
sustained interaction among national and international researchers in the country,
promoted by IM-AGIMB, there was a sharp increase both in quality and in the number of
research articles published by the group, as it can be seen in the full report of activities in
the area.
The connection between commutative algebra and algebraic geometry goes beyond the
ordinary bore of language transposition. In more recent years, this intimacy has grown into
a considerable body of information and even more solemn topics such as characteristic p
methods, have found deep applications throughout the entire field. In Brazil, research in
these two kin areas was born in the spirit of close cooperation since its very inception. Its
beginnings can be traced to no earlier than the mid seventies, thus placing it as very
recent amidst other traditional areas of mathematics in the country. Thanks to this
cohesive stirring the group has been successful in promoting activities within global
science initiatives, most specially this Millennium Institute. This institution played a key role
in stimulating the planning and the support of the following fundamental strategies for
progress in the area: specialized meetings; interchange with foreign institutions;
cooperation between established centers and emerging research groups; extending the
cooperation research with Latin American counterparts and students and research
projects. A substantial part of the scientific results by the group goes by way of a virtually
existing cooperative network throughout the country that includes researchers in more
than half a dozen institutions. The present number of pre-doctoral and doctoral students is
still shy – 20 circa – but it is expected to grow in the foreseeable future in the presence of
the above strategies, for which the Millennium shall continue to play a key role. A very
prominent feature of the group is its foreign collaboration portfolio, including more than 30
renowned institutions spread through 11 countries. In the last two and a half years the
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publication output by members of the Millennium group accounts for nearly 60 papers
published or accepted for publication in reputed international journals. This gives an
average of 5 papers per capita during the period or 2 a year. This publication hinges upon
a variety of themes, ranging from Rees algebras of special modules to module theoretic
criteria of birationality, from arithmetical and geometric aspects of curve theory to moduli
theory, from elliptic curves to rational points of curves in characteristic p, from arithmetic of
fields to Witt theory, from D-modules to algebraic and holomorphic foliations to differential
simplicity of rings, from general algebraic theory of singularities to Bernstein—Sato
polynomials, from vector bundles over curves to enumerative geometry, classification of
varieties and Mori theory.
Dynamical Systems
Over the last 30 months, the Brazilian school on Dynamical Systems has obtained
excellent results, in line with the reputation this area has attained in the world scenario:
publication of research papers in the best journals, intense training of young and very
active researchers, strong collaboration with other research groups all over the world,
organization of scientific meetings, and participation of its researchers as invited speakers
in the major international events. On the scientific level, the recent developments bring us
close to a broad theory of so-called chaotic dynamical systems, both ergodic and
geometric, as well as to a deeper understanding of holomorphic foliations and vector
fields. On another level, we observe the dissemination of very good research activity
throughout Brazil, with the creation of small groups of young researchers in Emerging
Centers, and the reinforcement of research activity in main centers. Much of this has
greatly benefited from the action of the Millenium Institute IM-AGIMB which, besides
adding resources and increasing the activities, has brought much needed stimulus and
stability to the planning of the groups initiatives, ensuring their viability in due time and,
thus, allowing for a new level of global advancement of the area and optimal use of
resources. Moreover, the excellent impact the Institute has been having on its Emerging
Centers has, no doubt, much to do with the creation of conditions for the installation of
young dynamicists in institutions located in other regions of the country, globally expanding
in a qualified way, this scientific area in Brazil.
Topology and Singularity Theory
Over the last 30 months, the areas of Topology and Singularity Theory obtained excellent
scientific progress, in large part due to the promotion of the IM-AGIMB. The stimulus of
being part of such an excellent virtual institute along with other leaders of mathematics in
Brazil, as well as the possibility of planning activities with assurance of support and the
flexibility and ease of carrying them out, were decisive for this progress, not only in
established research groups, but also in associated groups in various other Brazilian
institutions. Scientific productivity in the areas of topology and singularities included about
120 papers and books published or accepted for publication in international periodicals.
The formation of new researchers in this period was very good, with the defense of 21
doctoral theses, 7 in singularity theory and 14 in topology. The excellent evolution of
research in these two areas is evident in view of the significant number of publications in
outstanding periodicals, such as Topology, Transactions of the AMS, Compositio
Mathematica, Astèrisque, J. für die reine und ang. Math., Ann. Inst. Fourier, and Ergodic
Theory Dynamical Systems, among others.
13
Combinatorics
The Millenium Institute (IM-AGIMB) has strongly supported the scientific activities in
combinatorics and algorithms in the country. Broadly speaking, its support has generally
been in the form of promoting specialized scientific meetings and in the form of promoting
visits of renowned researchers to the country. For example, IM-AGIMB was instrumental in
bringing to Brazil researchers such as N. Alon (Tel Aviv), B. Bollobás (Memphis and
Cambridge), P. Pudlák (Czech Acad. Sciences), B. Reed (McGill), and V. Rödl (Emory
Univ.), all speakers at the International Congresses of Mathematicians, and G. Cornuéjols
(Carnegie Mellon) and A. Frieze (Carnegie Mellon), both winners of the Fulkerson Prize.
Despite the fact that the area of combinatorics and algorithms has strong roots in the
country and the fact that the research carried out in Brazil is internationally recognized, the
area still needs to grow considerably. It usually comprises researchers working in
mathematics and computer science departments. IM-AGIMB has induced a much stronger
interaction among researchers and students from diverse institutions, and subareas, with a
varied range of interests, thus very much supporting combinatorics as a whole in the
country. In brief, IM-AGIMB has been instrumental to the substantial advancement of the
area in Brazil.
Operator Algebras/Harmonic Analysis
The Millenium Institute IM-AGIMB promoted the visit of Vaughan Jones to Brazil,
specifically Florianópolis and Rio de Janeiro. He is one of the greatest specialists in the
area of Operator Algebras and its applications to Physics. In 1990 he was awarded the
Fields Medal, a unique distinction in the area of mathematics. His presence had a great
impact on the researchers and PhD students. Also, he led a joint important research
project with R. Exel of the Federal University of Santa Catarina. Moreover, his presence
also stimulated the advance of the area in two different fronts: the first concerns a
satisfactory description of an algebra considered to be of fundamental importance in the
understanding of applications to physics, such as Ising´s quantic model. The second front
concerns the development of techniques suggested by research in this area from the
analytic point of view to a pure algebraic context.
The research in Partial Differential Equations has made significant progress in the past
thirty months, with substantial improvement, both qualitative and quantitative, on its
publication record, in the conclusion of doctoral dissertations, in the implementation and
maturation of research and graduate education in emerging institutions, and in the
intensification of the scientific exchange between researchers from Brazilian institutions
and their colleagues from abroad. The creation of the Millenium Institute has played a
crucial role in this progress by making it possible to develop a global strategic planning of
scientific activities including meetings, Scientific Initiation and Post-Doctoral programs and
the support to emerging institutions in terms of bibliographic and computational
infrastructure, as well as the effective participation of their researchers in national events
and scientific cooperation. Among the broad research lines in Partial Differential
Equations, we highlight linear equations, nonlinear evolution equations and nonlinear
elliptic equations as areas of particularly well developed activity, with large research
production and with consolidated and geographically well-distributed groups. In the
14
framework of the Millenium Institute, 5 workshops were organized in partial differential
equations, several complex variables, non-linear differential equations, elliptic equations
and finally in differential equations: theory, computation and applications. There was also a
symposium on scattering and spectral theory. Besides those, several schools were
organized, one of them having the participation of researchers from Brazil, Chile and
Argentina. It is to be noticed that one of the workshops as well as a colloquium, took place
in Centers in Development, jointly the Federal Universities of Campina Grande and
Paraíba and in the Federal University of Pará. As can be seen from the individual reports
by organizers of the Millenium Institute activities, there has been substantial improvement
of the scientific output in the field of Partial Differential Equations by Brazilian researchers
as stated above. This increased productivity has been felt both in the established and in
the emerging institutions. We attribute this improvement to the talent of the young
scientists coming out of the graduate programs in the area in Brazil, to the intensification of
the scientific exchange of Brazilian researchers from different institutions among
themselves and with foreign distinguished colleagues and to a remarkable broadened
horizon of planning for scientific activities, brought about by the Millenium Institute.
Mathematical Economics and Finances
The main topics of research in mathematical economics are general equilibrium with
incomplete markets and bankruptcy, asymmetric information problems without the singlecrossing property, equilibria in security markets, collaterals, models with a supra national
currency. Due to the great interest of both the public and private sectors, the area of
Mathematical Economics is important for the development of the country. But, a main
difficulty for the establishment of a sufficient large scientific-academic community in the
area must be mentioned. This situation is basically due to the fact that young scientists are
offered better salaries by the private and public sectors or by academic institutions abroad.
Even so, the number of PhD´s formed in the country is increasing, as well as the number
of articles published in the best journals, notstandingly a prominent role played by former
IMPA´s students. The role of IM-AGIMB has been essential for the clear success of the
area in Brazil in recent years, to stimulate the planning of an important workshop, and to
high level scientific cooperation.
Probability
During the period of the existence of IM-AGIMB, research in the area of Probability has
greatly advanced in Brazil in various theoretical topics and applications, in special
statistical mechanics. It deserves to be mentioned the success obtained in the study of
disordered systems, in particular in the treatment of random walks in random
environments, and growth models out of equilibrium, as well as in the hydro-dynamical
description of particle systems, perfect simulation, convergence of random trees to
structures such as the Brownian web, interfaces of competition, besides applications to
linguistics. The role of IM-AGIMB has been critical to such a success. It has promoted a
number of high level scientific meetings, as well as research projects arising from scientific
cooperation within the country and with foreign partners. In particular, the interchange with
colleagues from Latin America has greatly intensified. Another key fact has been the
promotion of an intense participation of Ph.D. students and young Post-Doctoral
researchers in all the activities, resulting in an enlargement of the research community.
15
Petroleum Science
It is fair to state that IM-AGIMB was instrumental in promoting scientific interchange
among the small number of researchers in Brazil interested in mathematical aspects of
petroleum science, and between them and foreign distinguished colleagues, both by
planning and promoting symposia and workshops and mutual collaborative visits and joint
research. It has fostered further scientific links between these researchers and the
international community. As a result, a significantly better understanding of the several
multiscale phenomena that occur in flow in porous media has been reached, especially in
the nonlinear scale-up problem in petroleum reservoirs. Progress has been made in
understanding the wave structure of thermal flow in reservoirs, which is important for the
recovery of the existing untouched reserves of very viscous oil. IM-AGIMB has also
fostered the advent of a greater number of Ph.D. students in the area of Petroleum
Science.
IM-AGIMB has been giving an important contribution to the expansion of the Brazilian
scientific collaboration with mathematicians from several countries in Latin America:
Argentina, Bolivia, Chile, Colombia, México, Peru, Uruguay e Venezuela. As planned in
the original project of IM-AGIMB, two kinds of actions have been conceived and are taking
place to consolidate and up-grade substantially the cooperation of Brazilian mathematics
with Latin America:
•
•
Tutorial missions at an introductory level, directed to young undergraduate students of
the neighboring countries and advanced level tutorial missions, directed to advance
undergraduate and graduate students, as well as researchers.
Visits of Latin American researchers to Brazil to collaborate with local mathematicians
in research projects and to participate in congresses, workshops and in Brazilian PostDoctoral programs.
As a consequence, the number of joint research work, visits and missions has increased
substantially contributing to a general research environment in mathematics in the region.
Emerging Centers
One of the fundamental tasks of IM-AGIMB is to support consolidating high level quality
research and teaching, especially at graduate level, in Emerging Centers in the Northern,
Northeastern and Central-West regions of Brazil.
The new concept presented here is that research groups in such Centers belong to the
same Virtual Institute of Excellence that comprises many of the more advanced groups in
the country. This provides a great stimulus to the Brazilian mathematical community as a
whole, in the sense of a global and integrated advancement as suggested by the very
name of the Institute.
The Emerging Centers have been able to plan their activities every year, or even for longer
periods, like for instance visits of researchers from national institutions or from abroad,
participation of their members in events and research activities in other national centers
and the acquisition of some books for their libraries and computational equipment. A fair
16
number of CNPq’s Scientific Initiation fellowhips have been provided to them via IMAGIMB.
At the beginning of the Institute’s activities, in January 2002, we had nine Emerging
Centers. Now we have twelve, and the last one in fact is a Virtual Emerging Center with
research groups from four different institutions. This gives an idea of the enthusiasm of
these IM-AGIMB groups from the Northern, Northeastern and Central-Western, together
with that of Federal University of Paraná, to be working together towards the advancement
of mathematics. A concrete result in this direction is that since the start of IM-AGIMB, four
Emerging Centers of them had their M.Sc. programs officially accredited by CAPES, the
Agency from the Ministry of Education that supervises the graduate programs in Brazil.
17
Reports
Areas of Activities
Mathematical Instruction
Olympiads in mathematics are under way in some 85 countries and they occur on national,
regional and international scales. If properly structured Olympiads may serve as major
instruments for promoting sciences to young students. They are vehicles for improvement
of science teacher’s skills, and they aid in the detection of young scientific talents. To
achieve these three goals, the Olympiads should be large-scale events in each country, at
several grade levels and in three different stages at each level. The first test is very
friendly to students and their teachers, with many winners and simple prizes. The second
stage involves those who performed well in the first stage. Finally, a third stage determines
the best talents, who then compete internationally and are awarded fellowships for further
science training. This is precisely the structure of the Brazilian National Mathematical
Olympiads promoted by the Brazilian Mathematical Society and the National Council for
Scientific and Technological Development – CNPq. IM-AGIMB has been a new partner in
this important activity with two goals: to promote regional or state Olympiads within Brazil
and to expand the Brazilian participation in international competitions, specially the
International Mathematics Competition for University Students. IM-AGIMG´s contribution
lead to a participation of more than 130,000 students in the Regional Olympiads in
different states of Brazil, as well as to excellent performances at the International
Mathematics Competition for University Students, including being awarded a golden medal
in 2004.
Incentive to the Regional Olympiads in Brazil in 2002
16 Regional Olympiads took place in Brazil, with the participation of 2.796 schools and a
total of 83,417 students of elementary and high schools.
Regional Olympiads
V Olimpíada de Matemática UNIVATES
III Olimpíada Metropolitana de Matemática
Olimpíada de Matemática - Fase Regional Bahia 2002
XV Olimpíada Campinense de Matemática
V Olimpíada Regional de Matemática de Santa Catarina
Olimpíada Paulista de Matemática 2002
Olimpíada Regional de Matemática Grande Porto Alegre
2002
XI Olimpíada de Matemática do Estado de Goiás
Olimpíada Capixaba de Matemática 2002
Olimpíada Paraense de Matemática 2002
Olimpíada de Matemática do Estado do Rio de Janeiro 2002
II Olimpíada Piauiense de Matemática
Olimpíada Mineira de Matemática 2002
18
Schools
102
30
167
60
40
900
20
Students
2.960
460
3.000
2.510
1.000
35.000
1.200
500
267
20
230
25
350
1.800
17.792
2.500
3.000
1.049
4.000
Olimpíada Pessoense de Matemática
XIII Olimpíada de Matemática do Rio Grande do Norte
Olimpíada Cearense de Matemática 2002
Total
35
30
20
2.796
350
1.500
2.500
83.417
Regional Olympiads
I Olimpíada Alagoana de Matemática
VI Olimpíada de Matemática UNIVATES
IV Olimpíada Metropolitana de Matemática
XVI Olimpíada Campinense de Matemática
VI Olimpíada Regional de Matemática de Santa Catarina
Olimpíada Pernambucana de Matemática "Ruy
Luís Gomes" 2003
2003
XII Olimpíada de Matemática do Estado de Goiás
Olimpíada Capixaba de Matemática 2003
Olimpíada de Matemática do Estado do RJ 2003
III Olimpíada Piauiense de Matemática
XIV Olimpíada de Matemática do Rio Grande do Norte
Olimpíada Cearense de Matemática 2003
Total
Schools
19
68
41
167
204
102
1100
40
Students
490
5.556
550
2.830
3.000
5.074
45.000
2.400
60
2.400
573
312
17
30
30
70
20
35
40
2.928
2.400
20.944
1.500
200
1.850
4.055
1.500
1.791
6.850
108.390
Regional Olympiads
II Olimpíada Alagoana de Matemática
VII Olimpíada de Matemática UNIVATES
V Olimpíada Metropolitana de Matemática
XVII Olimpíada Campinense de Matemática
VII Olimpíada Regional de Matemática de Santa Catarina
Olimpíada Pernambucana de Matemática "Ruy Luís Gomes"
2003
2003
XIII Olimpíada de Matemática do Estado de Goiás
IV Olimpíada Piauiense de Matemática
Olimpíada Cearense de Matemática - 2003
19
Schools
25
100
70
300
60
126
1.500
110
Students
600
6.820
600
5.000
2.500
4.000
60.000
5.500
80
3.000
300
17
48
450
35
180
3.000
1.956
2.500
4.500
1.500
20.000
Olimpíada de Matemática da Região do ABC
Olimpíada de Matemática de Rio Preto
Olimpíada Regional de Matemática do Litoral Norte do Rio
Grande do Sul
Olimpíada Regional de Matemática da Unochapecó
Olimpíadas Sergipanas de Matemática
Total
20
32
115
200
1.500
2.500
81
200
3.849
4.000
2.000
131.676
International Olympiads
The participation of Brazil at the International Mathematical Olympiads has grown
exponentially, including the International Olympiad, the Ibero-American Olympiad, ConeSul, Ibero-American in Mathematics, the International Mathematical Olympiads for
University Students.
May Olympiads
This competition organized for young students is held in two levels: Level 1 for students up
to 13 years old and Level 2 for students up to 15 years old, from Latin America countries,
Spain and Portugal. In Brazil, this Olympiad is only for those students that have been
awarded in the Brazilian Mathematics Olympiads (Golden, Silver and Bronze Medals and
Honor Citation. The tests of the selected students are sent to the Organizing Committee in
Argentina, where the final classification is processed.
In 2002, 2003 and 2004, Brazil got the first place in the general classification by countries,
obtaining the maximum number of possible medals in each event (1 Golden Medal, 2
Silver Medals, 3 Bronze Medals and 4 Honor Citation in each participation)
Cone Sul Mathematics Olympiads
It is an international competition in which countries from the South America South Cone
take part, represented by 4 students teams that are not yet 16 years old until December
31st. of the year before the celebration of the Olympiad.
2002, Fortaleza - CE: Brazil was the fist among all participating countries, winning all the
golden medals of the competition. 3 Golden Medals and one Bronze Medal.
2003, Ica - Peru: Again, the Brazilian team achieved the best ponctuation among the
participating countries. 1 Golden Medal and 3 Silver Medals.
2004, Assunção - Paraguai: 1 Golden Medal, 1 Silver Medal and 2 Bronze Medals.
Ibero-American Mathematics Olympiads - OIM
It is an international competition in which the countries of Latin American, Spain and
Portugal participate, represented by teams of at most 4 students under the age of 18 years
until December 31st of the previous Olympiad.
2002, San Salvador - El Salvador: Brazil - 3 Golden Medals and 1 Silver Medal.
2003, Mar del Plata - Argentina: Brazil - 2 Golden Medals, 1 Silver Medal and 1 Bronze
Medal.
2004, Castellón - Spain: Brazil – Participants: 4 Golden Medals!
20
International Mathematics Olympiads - IMO
Organized since 1959, it is the most important international competition. About 100
countries participate in that competition, represented by teams of up to 6 secondary school
tudents or that have not yet entered at the University or equivalent, at the date of the
celebration of the Olympiad.
In the last four years, Brazil has consistently achieved performance. Of the 24 students
that participated in the last four years, only two didn't get medals, but, even so, they were
awarded Honor Citations.
2002, Glasgow - UK: Brazil - 1 Silver Medal and 5 Bronze Medals.
2003, Tóquio - Japão: Brazil - 1 Silver Medal, 3 Bronze Medals de Bronze, 2 Honor
Citations.
2004, Atenas - Grécia: Brazil - 2 Silver Medals and 4 Bronze Medals.
International Mathematics Competition for University Students - IMC
In 2003 Brazil participated for the first time of the International Mathematical Competition
for University Students with a team formed by 8 students from Brazilian universities (3
students of ITA, 1 student of UFRJ, 1 student of UNICAMP, 2 students of IME and 1
student of UFSC). In this competition main universities in the world participate such as, for
example, Cambridge, École Polytechnique, Institute Max Plank, Technion Institute,
Massachusetts Institute of Tecnology (MIT), Oxford University, Universidade Complutense
of Madri and University of Moscow.
The event took place from July 25 to July 31 through the University Dribble-Bolyai, in Cluj
Napoca (Romania). 3 Silver Medals, 3 Bronze Medals, and 2 Honor Citations were
awarded to Brazilian.
In 2004 Brazil participated for the second time in this competition with a team of 11
students (2 students of ITA, 3 students of IME, 1 student of UFRJ, 1 student of UNICAMP,
1 student from UFPI, 1 student from UFBA, 1 student from UFC and 1 student from
UFGRS). We obtaining an excellent result once again: 1 Golden Medal, 3 Silver Medals, 3
Bronze Medals and 4 Honor Citations. Yuri Gomes Lima, a student from the Federal
University of Ceará was awarded a Golden Medal and was classified globally in first
place.
Ibero-American Mathematics Olympiads of Universities - OIMU
It is an international competition where the participants should not possess a University
and should be registered at a University as an undergraduate student. Brazil organizes
this competition since 2002.
In 2002 and 2003 Brazil got the first place in the general classification obtaining the
maximum of medals in each competition: 1 Gold Medal, 2 Silver Medals, 4 Bronze Medals
and 3 Honor Citations.
21
Thematic advances reached in Climate Studies
The most important conceptual advances reached in this contribution to the IM over the
last 30 months was the theoretical discovery of multiple stable equilibria in the biomeclimate coupled system for Tropical South America, along the lines of recent theoretical
and experimental investigation on abrupt transitions of ecosystems between contrasting
stable states. The interaction of the vegetated surface and the atmosphere through the
turbulent fluxes of momentum, heat, water vapor and other substances is highly nonlinear.
On the other hand, it has been known for a long time that the geographical distribution of
vegetation types (biomes) depends also nonlinearly on climate parameters. Therefore,
theoretically one could expect that the coupled biome-climate system to exhibit multiple
states. CPTEC Atmospheric General Circulation (AGCM), coupled to a biome model
recently developed at CPTEC (Oyama and Nobre, 2004b), was used to numerically search
for multiple biome-climate stable equilibria. Two stable states were found when the
numerical calculations were started with two contrasting boundary conditions as global
vegetation specification at initial time (Oyama and Nobre, 2003): when all global biomes
were initially specified as tropical Forest, after 5 iterations of the coupled biome-AGCM
model, a global distribution of biomes quite similar to the natural distribution of biomes as
of the present was found. This was expected since the current distribution of biomes is a
stable solution of the biome-climate space. On the other hand, when the initial biomes
were globally set to be desert (absence of vegetation), a second, somewhat different state,
was reached for Tropical South America. In the latter, savannas cover most of eastern
Amazonia and semi-deserts replace a large portion of the caatinga (dry scrubland) of
Northeast Brazil. A sensitivity test was carried out (Oyama and Nobre, 2004a) by replacing
in CPTEC AGCM the caatinga vegetation by deserts. The numerical simulation having the
semi-arid portion of NE Brazil replaced by deserts showed reduction of rainfall. That
supports qualitatively the second equilibrium state found for NE Brazil having semi-deserts
as the equilibrium biome. Paleovegetation reconstructions for 21kBP (last glacial
maximum) show savannas dominating most of the eastern Amazonia. That provides some
indirect validation of the realism of the second biome-climate equilibria for Amazonia. It
must be highlighted that, before this finding, there was only one proposed biome-climate
stable equilibria for the planet, the Sahara-Sahel desert. The continuity of the investigation
is to study the transient case. That is, to determine the character and magnitude of
external forcing that could abruptly (“catastrophically”) tip the balance towards the second
state. Such forcing could be stochastic (e.g., a long period of pronounced droughts
affecting the region) or external perturbations (e.g., deforestation or global warming) in
interaction with the internal dynamics of the coupled system. Various perturbations are
decreasing the system’s resilience, making it less difficult to reach the abrupt transition to
the second equilibrium state. For example, the various scenarios of global warming for
2100 indicate substantial alterations in the biomes of Tropical South America (Nobre et al.,
2004): tendency of “savanization” of Amazonia and desertification of NE Brazil. There is
considerable theoretical and practical interest to find out whether such changes would
occur gradually and slowly or, alternatively, whether they could happen abruptly. These
scenarios have implications for environmental policies on conservation and natural
resources utilization for both Amazonia and NE Brazil.
22
Thematic advances reached in Weather Prediction
The Weather Prediction and Climate Group continues to focus on improving the efficiency
of numerical methods used in simulation models for the atmospheric climate system as
well as theoretical aspects for the atmospheric flow. In particular those connected with
nonlinear effects and also originated from perturbation of the atmospheric flow.
Developing a semi-Lagrangian scheme for global modelling
This project has in mind enabling the Brazilian Center for Weather Prediction and Climate
Studies (CPTEC; of the National Institute of Space Research (INPE)) with a modern and
efficient operational code.
The collaboration between CPTEC/INPE, IAG/USP, IME/USP and IMPA is still taking
place in the final phase of the CPTEC project of Modernizing and Optimizing the global
CPTEC code. This Development project has also an Applied Mathematics Research side
to it as indicated below.
This project involved research professors, postdocs, graduate students and computing
engineers/computer scientists. The institutions involved were coordinated by Dr.J.L.
Bonatti (CPTEC/INPE), with local coordination by Prof. P.L.D. da Silva (IAG/USP), Dr. J.
Panetta (CPTEC/INPE), Prof . S. Barros (IME/USP), Prof. D. Marchesin, Prof. A. Nachbin,
Dra. M. Moura Carmona (IMPA) and Prof. B. Costa (UFRJ; Federal University of Rio de
Janeiro) which has been involved through IMPA.
§
Coupling models
A mesoscale atmospheric model was coupled to a simplified photochemistry model in
order to simulate the impact of urban emissions in the formation of ozone. A set of 20
prognostic equations forming a stiff system, highly non-linear, had to be efficiently solved
in order to produce a FORTRAN code which could be used in operational forecasting of air
quality in São Paulo. The numerical solution with time splitting, coupled to a semi-implicit
numerical scheme, lead to an efficient numerical code in a distributed memory computer
(PC cluster). The numerical experiments indicated that through the non-linear role of the
photochemistry is responsible for the production of high ozone levels downstream of the
major urban sources.
Last year, the same mesoscale model used in the photochemistry modeling was coupled
to a gas/particle emission module for the simulation of biomass burning. In the last year,
this model was coupled to highly complete radiation model that allows the study of the
thermodynamical impact of the aerosol load produced by biomass burning. It has been
shown that the plume produced by biomass burning in the border of the Amazon can
potentially decrease the precipitation thousands of kilometers from the burning area.
Significant temperature decrease has also been shown. plume of associated to the
providedgas and particle emission model, where the emissions are generated by burning
biomass. The group in formed by : Dr. Saulo Freitas and Dr. Karla Longo from CPTEC and
Dr. Edmilson Freitas and Dr. Pedro L. da Silva Dias from IAG/USP). The development of
the numerical schemes was based on discussions with Dr. Saulo Barros from IME/USP.
A dynamical vegetation model was successfully coupled to the mesoscale atmospheric
model with the biomass burning aerosols emission module. It has been shown that the
non-linear effects associated to the interaction between the aerosols, radiation and
vegetation are responsible fort significant changes in the vegetation properties and the
precipitation regime in the transition season between the dry and wet periods in
southwestern Amazonia.
23
§
Nonlinear interactions
The work on non-linear resonance among tropical waves in the atmosphere has produced
a possible explanation for the observed spectral peak in the intraseasonal time scale (2060 day period) in the tropical atmosphere. It has been shown that the interaction of two
resonant triads with a coupling high frequency mode (which represents the convective
forcing) may lead to a significant response in the intraseasonal time scale. The explanation
is based on a nonlinear interaction mechanism between tropical and equatorial waves. A
Galerkin solution method, based on the eigenfunctions of the linear operator, was used to
study the flux of energy between several types of waves supported by the system.
An extension of this work is in progress as part of the doctoral research of Carlos F.M.
Raupp and IAG/USP in collaboration with LNCC researchers. This work intends to explore
the nonlinear interaction mechanisms between vertical modes in a more realistic
atmospheric model.
The identification of the non-linear effects in complex numerical models has been explored
through analysis techniques. In particular, the combined effect of the heat island breeze,
topography and aerosols in urban areas in São Paulo has been explored though the
integration of a complex mesoscale atmospheric model coupled to a urban particle
emission module with interaction radiative effects.
§ Optimization of atmospheric simulators for parallel computing
This activity has as final goal the increase of efficiency for the parallel version of the
Regional Atmospheric Modelling System – RAMS model, widely used in Brazil by research
centers for meteorological processes in the regional scale. This work continues under the
coordination of Prof. Saulo Barros no IME/USP with the collaboration of Prof. Marcos
Dimas Gubitoso. Several code components were identified as requiring an optimization
effort along with changes in the interpolation schemes and operation sequences which
made the code more robust and efficient. This effort was in great part supported by FINEP
(a federal funding agency) aiming an efficient code that could be distributed to regional
centers for weather prediction and climate studies, which are sponsored by the Ministry of
Science and Technology (MCT) within the program Weather and Climate coordinated by
CPTEC.
Thematic advances reached in Waves in Heterogeneous Media
In this area attention was focused on dispersive and nonlinear waves interacting with an
inhomogeneous medium, namely a highly varying topography. This theme of Applied
Mathematics analyses partial differential equations with highly oscillatory coefficients.
These equations are models in hydrodynamics and are of interest in Meteorology and
Oceanography. This activity of the IM-AGIMB has had a good interaction with Theoretical
Physics. Results obtained by the group were the first mathematical theory concerning the
apparent diffusion and time-reversed refocusing (source reconstruction) in the context of
dispersive and also nonlinear waves (Fouque et al. 2004; Fouque, Garnier e Nachbin
2003, 2004; Muñoz e Nachbin 2004a, 2004b, Nachbin e Solna 2003). Recently these
results were extended to dissipative systems (Garnier e Nachbin 2004). Also a very
important result was obtained in a PhD thesis at IMPA (Alfaro et al. 2004). Dr. Daniel
Alfaro (recently graduated at IMPA in May 2004) is starting a postdoc at the Mathematics
Department of the University of California at Irvine. In his thesis Alfaro studied the
robustness for time-reversal in the case of a (randomly) time varying random medium. This
is very important for true applications where the propagation medium is not static. The
24
mathematical modeling makes use of sophisticated asymptotic analysis of stochastic
differential equations, a theory developed over the past 30 years by Prof. George
Papanicolaou and collaborators. To emphasize the physical impact of the results in this
activity of the IM-AGIMB three letters regarding Waves in Heterogeneous Media were
accepted at the prestigious Physical Review Letters. One of these letters was published by
the former PhD student at IMPA, Dr. William Artiles, whose is now as a postdoc at the
Institute of Theoretical Physics, IFT/UNESP, São Paulo.
Events organized
Workshop on Ensemble Weather Forecasting. An initiative of the Milenium Institute
“Global and Integrated Advancement of the Brazilian Mathematics “ was held at the Center
for Weather Forecasting and Climate Studies, Cachoeira Paulista SP, Brazil, from
February 09 to 11, 2004. The event was joint effort of the Center for Weather Forecasting
and Climate Studies – CPTEC/INPE , Cachoeira Paulista, the Institute of Astronomy,
Geophysics and Atmospheric Sciences – University of São Paulo, São Paulo and the
Institute of Pure and Applied Mathematics – IMPA – Rio de Janeiro. About 80 participants
including 4 foreign speakers. A specific report is provided as an annex.
This workshop considered the three major approaches in ensemble forecasting: (a)
“Singular vector method”, (b) breeding of growing modes” and (c) “Empirical orthogonal
function method”. A final product of the workshop was a recommendation of a research
plan involving mathematicians, research and operational meteorologists aiming towards
the improvement of the weather forecasting capability in Brazil.
List of publications 2002-2004
1. Alfaro Vigo, D.G., Fouque, JP, Garnier, J., and Nachbin, A., Robustness of time
reversal for waves in time-dependent random media, accepted for publication in
Stochastic Processes and their Applications, 2004.
2. Artiles, W., and Nachbin, A., Nonlinear evolution of surface gravity waves over highly
variable depth, accepted for publication Physical Review Letters, 2004.
3. Fouque, JP, Garnier, J, Munoz Grajales, JC and Nachbin, A, Time reversing solitary
waves, Physical Review Letters, 92(9), 094502-1, 2004.
4. Fouque, JP, Garnier, J., and Nachbin, A., Shock structure due to stochastic forcing
and the time reversal of nonlinear waves, accepted for publication at Physica D, 2004.
5. Freitas S.R., K.M. Longo, M.A.F.Silva Dias, P.L. Silva Dias, F.S. Recuero, R.
Chatfield, E. Prins, P. Artaxo. Monitoring the Transport of Biomass Burning Emissions
in South America. Environmental Fluid Mechanics, 2004 (in press).
6. Garnier, J and Nachbin, A, The eddy viscosity for time reversing waves in a dissipative
environment, accepted for publication in the Physical Review Letters, 2004.
7. Muñoz Grajales, J.C. and Nachbin, A., Dispersive wave attenuation due to orographic
forcing, SIAM J. Appl. Math., 64(3), p.977-1001, 2004.
8. Muñoz Grajales, JC, and Nachbin, A., Stiff microscale forcing and solitary wave
refocusing, accepted for publication at the SIAM Multiscale Modeling and Simulation
journal, 2004.
25
9. Oyama, M. D. and Nobre, C.A, 2004a, Climatic consequences of a large scale
desertification in Northeast Brazil: a GCM simulation study, Journal of Climate (to be
published 15 August 2004).
10. Oyama, M. D. and Nobre, C. A., 2004b A simple potential vegetation model for
coupling with the Simple Biosphere Model (SiB). Revista Brasileira de Meteorologia (in
press).
11. Nobre, C. A., Oyama, M.D., Marengo, J.A., Oliveira, G.O., Salati, E. Impacts of
Climate Change Scenarios for 2091-2100 on the Biomes of South America. First
CLIVAR International Conference, Baltimore, USA, 21-25 June 2004 (pôster).
12. Nachbin, A., and Solna, K., Apparent diffusion due to orographic microstructure in
shallow water, Phys. Fluids, 15(1), p.66-77, 2003.
13. Oyama, M.D. and Nobre, C.A. A new climate-vegetation equilibrium state for Tropical
South America.Geophysical. Res. Letters, 30 (23), p.2199-2203. December, 2003.
14. Fouque, JP, Garnier, J. and Nachbin, A., Time reversal for dispersive waves in
random media, accepted at SIAM J. Appl. Math., 2003.
Ph.Ds. 2002-2004
1. Daniel G. Alfaro Vigo: Time-reversed acoustics in a randomly changing medium,
IMPA, 2004, (Advisor Prof. A. Nachbin).
2. Maria Autora dos Santos: Convecção na Amazônia: Variabilidade, efeitos e resposta
na circulação de grande escala. INPE, São José dos Campos, 2004 (Advisor Prof. C.
Nobre).
3. William Artiles Roqueta: Modelagem de ondas não lineares através do operador
Dirichlet-to-Neumann, IMPA, 2004 (Advisor Prof. A. Nachbin).
4. Claudine Dereczynski: Estudo dos Limites de Previsibilidade Climática para o Norte
do Nordeste, COPEE-UFRJ, Rio de Janeiro, 2004 (Advisor Prof. C. Nobre).
5. José de Arimatéia Fernandes: Grades heterogeneas na solução espectral das
equações de águas rasas, IMPA, 2004 (Advisor Prof. D. Marchesin).
6. Milton dos Santos Braitt: Métodos Semi-Lagrangeanos precisos para ondas de
Rossby com Orografia, IMPA, 2002 (Advisor Prof. D. Marchesin).
7. Paul Krause: Escoamentos Friccionais do Ar, IMPA, 2002 (Advisor Prof. D.
Marchesin).
8. Juan Carlos Muñoz Grajales: Dispersive wave attenuation and refocusing due to
disordered orographic forcing, IMPA, 2002 (Advisor Prof. A. Nachbin).
9. Marcos Oyama: Conseqüências Climáticas da Mudança de Vegetação do Nordeste
Brasileiro: Um Estudo de Modelagem. INPE, São José dos Campos, SP, 2002
(Advisor Prof. C. Nobre).
26
Control Theory
Control theory has a significant role to play in almost every branch of science and
engineering. It has contributed in a very fundamental way to the technological progress in
many areas, in recent decades. The classical theory (automatic control systems) has
been widely used in modern society and it ranges from simple application such as in the
temperature control to highly sophisticated systems such as airplanes and satellites. It is
accepted nowadays that advances in strategics topics such as complex network (which
includes high speed communications, power network and wireless communication),
manufacturing systems, speech recognition, robotics, image analysis and safety-critical
and high-integrity systems, among others, would be difficult without control methodologies,
which illustrate the importance and potential of the field. In addition, it has even had a
large impact on areas such as biological modeling and ecomomics.
In order to make the most of the interdisciplinary bent of control theory, “which shall be one
of the most important characteristic of the 21st century science”, it would be necessary to
enlarge and/or consolidate research groups in control theory in Brazil. . There is no doubt
that huge strides have been made in turning these ideas into realities with IM-AGIMB
program. IM-AGIMB has contributed decisively to this aim by supporting conference
organization; visitor programs of highly qualified researchers; participation in conferences;
a post-doc program; meetings for joint research, inter alia. It is perhaps worth mentioning
here that these actions have contributed for an stimulating research atmosphere and an
efficient training of high level PhDs students.
The control activities of the IM-AGIMB has involved researchers from institutions such as
LNCC, UNICAMP and USP, which concentrate their research, essentially, on uncertain
dynamical systems control theory (UDCT) and Dynamics and Geometric Control Theory
(DGCT). The main researchers, by institutions are:
DSC/LNCC/MCT - Marcelo D. Fragoso and Carlos Emanuel de Souza (UDCT group)
LAC/USP - Oswaldo L. V. Costa (UDCT group)
FEE/UNICAMP - José C. Geromel and João Bosco R. Do Val (UDCT group)
DM/IMECC/UNICAMP - Luiz A. B. San Martin e Marco Antonio Teixeira and P.R.C.
Ruffino (GCT group).
An important feature of the IM-AGIMB is that it has, from the outset, strengthening the
interaction between the control group and various institutions, (which includes those that
participate of IM-AGIMB). We list below others institutions which have interacted with the
control group:
In South America: Ibilce/UNESP - Rio Preto, UEM-Maringá, UFG-Goiânia, Chile
(Antofagasta and Santiago), Chile (Universidade Técnica Frederico Santa Maria,
Valparaiso), Colômbia (Bucaramanga) and Argentina (Mar del Plata)
Other places: Caltech (USA), UA Barcelona (Espanha), Universidade da Borgonha
(França), Rouen (França), Laboratoire d'Analyse e de Architecture de Systemes
(LAAS/CNRS), Toulouse, (França), Université de Bordeaux I, Bordeaux, (França),
Imperial College (UK), Oxford (UK), Augsburg (Alemanha), Iowa (USA)e TechnionHaifa (Israel), University of Newcastle ( Austrália),
27
Department of Electrical Engineering - Systems, Tel-Aviv University (Israel), School of
Electrical Engineering, Nanyang University (Cingapura).
Regarding publication, the outcome has been a host of new important ideas and
techniques which has been published, or submitted for publication, in leading scientific
journals. The members of this group has published about 32 articles in journals such as,
SIAM Journal on Control and Optimization, Journal of Mathematical Analysis and
Applications, Stochastic Analysis and Applications, International Journal of Control,
International Journal of Robust and Nonlinear Control, Advances in Mathematics, Journal
of Symbolic Computation, Dynamical Systems: An International Journal, Bull. of Sc.
Mathematiques, inter alia. In this period, 2 books has been prepared and is due to be
published. Many articles, about 24, have been also presented in top conferences such as
IEEE Conference on Decision and Control, IFAC Conferences and American Control
Conferences.
Scientific Production 2002-2004
1. D. Leão Jr., M.D. Fragoso and P.R.C. Ruffino: Regular conditional probability,
disintegration of probability and Radon spaces. Proyecciones, 24(1), 15-29, 2004.
2. M.D. Fragoso and O.L.V. Costa, Mean Square Stabilizability of Continuous-Time
Linear Systems with Partial Information on the Markovian Jumping Parameters,
Stochastic Analysis and Applications, 22, 99-111, 2004.
3. M.D. Fragoso, Discussion on: On the Continuous Time-Varying JLQ Problem,
European Journal of Control, 10, 2004.
4. O.L.V. Costa and M.D. Fragoso, Comments on “Stochastic Stability of Jump Linear
Systems”, IEEE Transactions on Automatic Control, 49, 1414-1416, 2004.
5. O.L.V. Costa and F. Dufour. On the Poisson Equation for Piecewise Deterministic
Markov Processes, SIAM J. on Control & Optimization, 42, 985-1001, 2003.
6. J.B.R. do Val, C. Nespoli and Y.R.Z. Cáceres, Stochastic Stability for Markovian Jump
Linear Systems Associated with a Finite Number of Jump Times, Journal of
Mathematical Analysis and Applications, 285, 553-565, 2003.
7. C.E. de SOUZA and M.D. FRAGOSO, H-infinity Filtering for Discrete-Time Linear
Systems with Markovian Jumping Parameters, International Journal of Robust and
Nonlinear Control, 13, 1299-1316, 2003.
8. O.L.V. Costa and E.F. Tuesta, Finite Horizon Quadratic Optimal Control and a
Separation Principle for Markovian Jump Linear Systems, IEEE Transactions on
Automatic Control, 48, 1836-1842, 2003.
9. C. E. de Souza, C. E., Trofino and J. Oliveira, A Parametric Lyapunov Function
Approach to H-2 Analysis and Control of Linear Parameter-Dependent Systems, IEE
Proceedings-Control Theory And Applications, 150, 501-508, 2003.
10. J. Braga Barros and L.A.B. San Martin, Maximal chain transitive sets for local groups.
Boletim da Sociedade Paranaense de Matemática, 21, 113-125, 2003.
11. A.Jacquemard and M.A. Teixeira, Computer analysis of periodic orbits of
discontinuous fields. Journal of Symbolic Computation, 35, 617-636, 2003.
28
12. A.Jacquemard and M.A. Teixeira, On singularities of discontinuous vector fields, Bull.
of Sc. Mathematiques, 127(7), 611-633, 2003.
13. M.A.N. Fernandes and L.A.B. San Martin, Geometric properties of invariant
connections on Sl(n,R)/SO(n). Journal of Geometry and Physics, 47(2-3), 369-377,
2003.
14. P.E. McSharry and P.R.C. Ruffino, Asymptotic angular stability in non-linear systems:
rotation numbers and winding numbers, Dynamical Systems: An International Journal,
18(3), 191- 200, 2003.
15. L.A.B. San Martin and C.J.C. Negreiros, Invariant Almost Hermitian structures on flag
manifolds, Advances in Mathematics, 178(2), 277-310, 2003.
16. J. Ribeiro Gonçalves and L.A.B. San Martin, The compression semigroup of a cone is
connected, Portugaliae Mathematica, 60(3), 2003.
17. C.E. de Souza and M.D. Fragoso. Robust H-infinity filtering for Uncertain Markovian
Jump Linear Systems, International Journal of Robust and Nonlinear Control, 12, 435446, 2002.
18. C.E. de Souza and M.D. Fragoso. H-infinity Filtering for Markovian Jump Linear
Systems, International Journal of Systems Sciences, 33, p.909-915, 2002.
19. D.P. De Farias, J.C. Geromel, J.B.R. Do Val, A Note on the Robust Control of Markov
Jump Linear Uncertain Systems, Optimal Control Applications & Methods, 23, p.105112, 2002.
20. E. F. Costa and J. B. R. do Val. On the Observability and Detectability of ContinuousTime Markov Jump Linear Systems, SIAM J. on Control & Optimization, 41, 12951314, 2002.
21. E.F. Costa, J.B.R. do Val, Weak Detectability and the Linear Quadratic Control
Problem of Discrete-time Markov Jump Linear Systems, International Journal of
Control, 75, 1282-1292, 2002.
22. F.A. Cuzzola, J.C. Geromel, M. Morari, An Improved Approach for Constrained Robust
Model Predictive Control, Automatica, 38, 1183-1189, 2002.
23. J.B.R. Do Val, E.F. Costa, Solutions for the Linear Quadratic Control Problem of
Markov Jump Linear Systems, Journal of Optimization Theory and Applications, 114,
69-96, 2002.
24. J.B.R. Do Val, J.C. Geromel, A.P.C. Gonçalves, The H-2 Control for Jump Linear
Systems: Cluster Observations of the Markov State, Automatica, 38, 343-349, 2002.
25. J.B.R. Do Val, M.G. Andrade, On Mean Value Solutions for the Helmholtz Equation on
Square Grids, Applied Numerical Mathematics, 4, 2002, 459-479.
26. J.C. Geromel, M.C. De Oliveira, J. Bernussou, Robust Filtering of Discrete-time Linear
Systems with Parameter Dependent Lyapunov Functions, SIAM Journal on Control
and Optimization, 4, 700-711, 2002.
27. M.C. De Oliveira, J.C. Geromel, J. Bernussou, Extended H-2 and H-Infinity Norm
Characterizations and Controller Parametrizations for Discrete-time Systems,
International Journal of Control, 75, 666-679, 2002.
29
28. M.C. De Oliveira, J.C. Geromel, L. Hsu, A New Absolute Stability Test for Systems
with State-Dependent Perturbations, Internat. Journal of Robust and Nonlinear
Control, 12, 1209-1226, 2002.
29. M.D. Fragoso and J. Baczynski. Lyapunov Coupled Equations for Continuous-time
Infinite Markov Jump Linear Systems, Journal of Mathematical Analysis and
Applications, 274, 319-335, 2002.
30. M.D. Fragoso and J. Baczynski. Stochastic Versus Mean Square Stability in
Continuous Time Linear Infinite Markov Jump Parameters Systems, Stochastic
Analysis and Applications, 20, 346-356, 2002.
31. O.L.V. Costa, A.C. Paiva, Robust Portfolio Selection Using Linear Matrix Inequalities,
Journal of Economic Dynamics and Control, 26, 889-909, 2002.
32. O.L.V. Costa, J.C.C. Aya, Monte Carlo TD (lambda)-Methods for the Optimal Control
of Discrete-Time Markovian Jump Linear Systems, Automatica, 38, 217-225, 2002.
33. O.L.V. Costa, R.B. Nabholz, A Linear Matrix Inequalities Approach to Robust MeanSemivaraince Portfolio Optimization, Computational Methods in Decision-Making,
Economics and Finance (editores: E.J. Kontoghiorghes, B. Rustem e S. Siokos,
Kluwer Applied Optimization Series, 74, 2002, 87-105.
34. O.L.V. Costa, S. Guerra, Robust Linear Filtering for Discrete-Time Hybrid Markov
Linear Systems, International Journal of Control, 75, 712-727, 2002.
35. O.L.V. Costa, S. Guerra, Stationary Filter for Linear Minimum Mean Square Error
Estimator of Discrete-Time Markovian Jump Systems, IEEE Transactions on
Automatic Control, 47, 1351-1356, 2002.
Books
1.
J.C. Geromel, A.G.B. Palhares, Análise Linear de Sistemas Dinâmicos: Teoria,
Ensaios
Práticos e Exercícios, ISBN 85-212-0335-7, 376 p., Edited by Edgard
Blücher Ltda (to be published in 2004).
2.
O.L.V. Costa, MD. Fragoso, R. Paulino, Discrete-Time Markovian Jump Linear
Systems, Springer-Verlag, Londres, Inglaterra (to be published in 2004).
Articles Accepted for publication
1. C. Buzzi and M.A. Teixeira: Time-reversible Hamiltonian vector fields with sympletic
symmetries. J. of Dyn. and Diff. Eq, 2004.
2. C. Buzzi, P.R. Silva and M.A. Teixeira Singular perturbation problems for timereversible systems, Proceedings of AMS, 2004.
3. E.F. Costa, J.B.R. do Val, M.D. Fragoso, On a Detectability Concept of Discrete-Time
Infinite Markov Jump Linear Systems, Stochastic Analysis and Aplications, 2004.
4. E.F. Costa, J.B.R. do Val, M.D. Fragoso, A New Approach to Weak Detectability and
the LQ Problem of Discrete-Time Infinite Markov Jump Linear, SIAM Journal on
Control and Optimization, 2004.
5. A.Jacquemard and M.A. Teixeira, Invariant varieties for discontinuous vector fields,
Nonlineatrity, 2004.
30
6. N. Cohen, C.J.C. Negreiros, M. Paredes, S. Pinzón and L.A.B. San Martin: fStructures on the Classical Flag Manifold which Admit (1,2)-Symplectic Metrics.
Tohoku Math. J., 2004.
7. O. G. do Rocio and L.A.B. San Martin: Connected components of open semigroups in
semi-simple Lie groups. Semigroup Forum, 2004.
8. R. Garcia and M.A. Teixeira: Vector fields in manifolds with boundary and reversibilityna expository account. Qualitative Theory of Dynamical Systems, 2004.
9. S Mancini, M Manoel and M.A. Teixeira, Divergent diagrams of folds and simultaneous
conjugacy of involutions, Discrete and Continuos Dynamical Systems (DCDS), 2004.
10. V. Ayala, W. Kliemann and L.A.B. San Martin: Control sets and total positivity.
Semigroup Forum, 2004.
11. F. Colonius, L.A.B. San Martin and M. Spadini: Fundamental Semigroups for Local
Control Sets. Annali di Matematica Pura ed. Applicata, 2003.
12. E.A. Coayla-Teran. and P.R.C. Ruffino,
theorems, Stochastics and Dynamics.
Stochastic versions of Hartman-Grobman
Another relevant objective of the IM-AGIMB s the preparation of new generations of
researchers, which includes an efficient training of high level PhDs students. With this aim,
the following result has been obtained.
Thesis concluded
Ph.D. Theses
1. Adélia Conceição Diniz. Supervisor: L.A.B. San Martin. Imecc-Unicamp, April 2004.
2. Ronan Antonio dos Reis. Supervisor: L.A.B. San Martin. Imecc-Unicamp, January2004
3. Eduardo Fontoura Costa. Supervisor: J.B.R. do Val. FEE/UNICAMP, 2002
4. Esteban Fernandez Tuesta. Supervisor: O.L.V. Costa. EPUSP, 2003.
5. Eulina Coutinho Silva do Nascimento. Superviser: M.D. Fragoso. LNCC, 2003.
6. Eyup Kizil. Supervisor: L.A.B. San Martin. Imecc-Unicamp, April 2003.
7. Karina Acosta Barbosa. Supervisor: C.E. de Souza. UFSC, 2003.
8. Nei Carlos dos Santos Rocha. Supervisor: M.D. Fragoso. UFRJ, 2003.
9. Rita de Cássia de Jesus Silva. Advisor: L.A.B. San Martin. Imecc-Unicamp, April 2003.
10. Sofia Pinzón. Supervisor: C.J.C. Negreiros. Imecc-Unicamp, April 2003.
M.Sc. Theses
1. Germano Abud de Resende. Supervisor: M.A. Teixeira. IMECC, UNICAMP: March
2004.
2. Michael Viriato Araújo. Supervisor: O.L.V. Costa., EPUSP, 2004.
3. Guilherme Gonzalez Cronemberger Parente. Supervisor: O.L.V. Costa., EPUSP, 2003.
4. Marcos Vergés. Supervisor: M.A. Teixeira. IMECC-Unicamp: September 2003.
5. Margareth Aparecida De Souza Bueno. Supervisor: O.L.V. Costa., EPUSP, 2003.
6. Rodrigo De Barros Nabholz. Supervisor: O.L.V. Costa., EPUSP, 2003.
31
Post-Doctoral Activities
1. Leonardo Navarro. Supervisor: M.A. Teixeira, Fapesp.
2. Maria Alice Bertolim. Supervisor: K. Rezende, Fapesp.
3. Regilene Delazari Oliveira: Supervisor: Marco A Teixeira, CNPq.
4. Edson Alberto Coayla Terán. Supervisor: M.D. Fragoso, FAPERJ.
As part of the IM important idea of integration of strong research groups, the geometric
control group has been supported by the IM-AGIMB, and has organized an International
Conference on Geometric Control (CIMPA School and Workshop on Geometric NonLinear Control–14-23 july 2003 - http://www.ime.unicamp.br/~cntrl03/) which has brought
together most of the leading researcher in this area. In addition, the IM-AGIMB has
supported some control activities in the 24° Colóquio Brasileiro de Matemática. One
important corollary of this activity was the impressive impact on the young students
interested in the area.
More specific details on the organization of meeting are as follows:
CIMPA School and Workshop on Geometric Non-Linear Control
•
Attended the meeting around 149 researches, undergraduate and PhD students,
coming from a number of Brazilian institutions and from abroad (UNICAMP, USP,
UNESP, ITA, INPE, UEM, UFMG, UFRJ, LNCC, UFSC, FURG, UNB, UFPr, UIS,
FAC, SENAC, U.N. Córdoba, U. Buenos Aires e U.N. de la Plata da Argentina; U. de
la República (Uruguay); PUC-Perú; Universidad Del Valle e U.I. Santander da
Colômbia, Rhodes University -África do Sul, among others). It was lectured 5
minicourses, 6 plenary talking and a great number of research communications.
•
The Minicourses: (1) Introduction to geometric control, (2) Control design: Motion
planning and stabilization (R. Murray e P. Rouchon); (3) Control systems and
semigroups (L.A.B. San Martin), (4) Introduction to optimal control (H.J. Sussmann),
(5) Geometry of distribuitions (B. Jakubczyk).
•
Plenary lectures: (1) Sub-Riemannian Geodesics (O. R. Abib), (2) Dynamics and
Control (F. Colonius), (3) Stability of planning motion (R. Murray), (4) Planning
motion, output tracking and flatness (P. Rouchon), (5) Stochastic differential geometry
(P. Ruffino), (6) Optimal control and variational methods (H.J. Sussmann), The subRiemannian geometry of micro-swimming (J. Koiller).
LNCC Summer School (26th January – 19 February)
•
During the school there was a week dedicated to control activities, which included the
following Minicourses: (1) Optimal control: some applications in medicine (Takashi
Yoneyama – ITA), (2) Analyses and modeling of finance time series (Cristiano
Fernandes – PUC/RJ), (3) Introduction to models in population ecology (Michel Iskin –
LNCC)
32
IM-AGIMB program has not only given a decisive contribution to the success of the
control group via supporting their activities, but has also introduced a very important
element (in fact a key issue) that is the possibility of planning activities such as
conference, which sometimes requires a long period of time, before the meeting takes
place. Sometimes, this process may take two years and it is impossible to carry on without
the guarantee that the financial resources are there. An important feature of IM-AGIMB,
among others, is that it allows that financial support for such activities be guaranteed in a
flexible an agile manner, which are fundamental issues for the success of conference
organization.
Finally, hoping that this very successful program that is the IM-AGIMB continues for the
next three years, the control group plans as its general main priorities for the near future:
(1) Consolidate the prestige in the international community, via highly relevant scientific
contributions, participation in conferences and training of PhDs students (2) Organize
conferences, workshops, etc., (3) To carry out a special visiting program for top
researchers in important strategic research topics and (4) To bring together others local
research groups(specially those with a more application-oriented motivation).
33
Optimization
Continuous optimization in Brazil began a process of steady development in the eighties,
almost exclusively concentrated in the Rio de Janeiro and S. Paulo areas. During the last
two decades those research groups became strong and well connected to the international
community, while several smaller groups bloomed in all regions of the Country. By the turn
of the century there was good diversity in research lines, including theory, algorithms and
applications, but the community was scattered in the Country with no appropriate
discussion forum.
Cohesion in this community was then sought with the organization of Brazilian workshops
on continuous optimization, which started small and exclusively national. The last two
workshops, in 2002 and 2004, mark a new phase in the area: they were jointly organized
by the Millennium Institute and local committees, becoming now well attended international
meetings. The Millennium
Institute has also helped the area by supporting post-doc programs and by sponsoring
regional meetings, thus playing an important role in the progress of
Optimization in Brazil. Another key aspect of the importance of the Millennium Institute for
the recent sharp development of Optimization in Brazil was its encompassing support of
Centers in Development, that includes the Federal University of Paraná, as well as the
Federal Universities of Piauí in the North-Eastern and Goiás in the Center-West, regions
were scientific development is much needed. Two good level meetings are soon to take
place in the Paraná and Goiás Centers.
More specifically, during the last two and a half years, the area of Optimization in Brazil
attained a new milestone in the intense development process which started in the 1980's.
Among the main features of the current stage in the development of the area, we
emphasize:
1. Consolidation of the main activity centers, around the Optimization groups at the
universities of São Paulo, Campinas, Federal de Rio de Janeiro and at IMPA, each
one of which has already attained a critical mass, in terms of professors and/or
researchers, which ensures the continuity of their scientific production, the number of
PhD and MSc degrees granted, etc.
2. Growth of several emerging groups in institutions where research in the area is
relatively recent, but which exhibit already healthy marks of self-assurance,
independently of their links to the already consolidated centers. We point out the
groups at the federal universities of Santa Catarina, Goiás and Piauí.
3. High level of interaction among researchers in different institutions, synergizing the
production of each group and allowing the treatment of problems which require
expertise in several subareas. This interaction was strongly stimulated by the
existence of the Núcleo de Excelência em Otimização Contínua, created in 1998
within the program PRONEX (CNPq-FINEP) e renewed in 2003 within the program
PRONEX (CNPq-FAPERJ).
4. Strong standing in the international scene, as can be verified through the intense
participation of Brazilian researchers in meetings abroad, with the high number of coauthorships with foreign colleagues, and with the frequent visits of many of them to
34
Brazil, be it for attending meetings here or for longer term visits, in order to collaborate
with Brazilian scientists. As a sign of this international prestige, we mention that the
most important international periodic meeting in the area, the Symposium on
Mathematical Programming, held every three years, will take place in Rio de Janeiro in
2006, when it will meet for the first time ever in a Third World country.
5. Institutionalization of periodical Brazilian meetings in the area, through the Brazilian
Workshops on Continuous Optimization, five of which already held, since 1998,
alternating between the cities of Rio de Janeiro and Florianópolis. The sixth one will
take place in Goiânia, in July 2005.
We round up this brief description of the state of the Optimization in Brazil with some
comments on the main research activities in each of the most significant groups.
The IMPA group, consisting of A.N. Iusem, C. Sagastizábal, M.V. Solodov and B.F.
Svaiter, focused its research in the theoretical aspects of Optimization, addressing issues
like variational inequalities, equilibrium problems, vector-valued optimization, proximal
point methods, augmented Lagrangians, 2-regularity theory, infinite dimensional
optimization and non-smooth optimization. We should mention also C. Sagastizábal's
activities in real life applications, like the managing of the Brazilian electric sector.
The UFRJ group, centered in COPPE, whose main members are R. Burachik, J.
Herskovits, N. Maculan, P.R. de Oliveira and S. Scheimberg, focused its research in
issues like applications of continuous optimization to discrete problems (e.g. Lagrangian
relaxation), set-valued analysis, bilevel programming, etc. We emphasize a large number
of real life applications, e.g. to civil engineering (structural optimization).
The UNICAMP group, under the leadership of J.M. Martínez, with the participation of R.
Andreani, M.A. Diniz-Ehrhardt, A. Friedlander, F.A.M. Gomes, M.A. Gomes Ruggiero,
L.V.R. Lopes, M.P. Mello and S.A. Santos, is the most consolidated group in Brazil. It
focused its activity in the development of continuous optimization software, including the
implementation of several computational packages, like QUACAN and GENCAN, which
are competitive with the best foreign software. The also work on applications to several
areas, like optics (fine film optimization) chemistry (docking problems), etc.
The group at USP, whose senior member is C. Humes Jr., includes also E.G. Birgin, W.
Mascarenhas, M. Queiroz, P. Silva e Silva and J. Stern. It has worked in different
subareas, like the eigenvalue complementary problem, the flow assignment problem,
sums of maximal monotone operators, etc., and in applications to financing, to biology
(gene sequencing), etc.
The group at UFSC, in Florianópolis, under the leadership of C. Gonzaga, generated some
years ago highly relevant contributions to the theory of interior point methods for linear and
convex programming, with special emphasis on central paths, and more recently has
moved to other subjects like filter methods, non-coercive penalty functions, etc. It has also
worked on applications to electrc energy generation problems.
Th groups at UFG and UFPi, in Goiânia and Teresina, with the participation of J.X. da
Cruz Neto, O.P. Ferreira and L.R. Lucambio Pérez, work mainly on optimization in
riemannian manifolds.
The support of the Instituto do Milênio to activities in Optimization consisted mainly of its
contributions to the 4th and 5th Brazilian Workshops on Continuous Optimization, in July
2002 in Rio de Janeiro, and March 2004 in Florianópolis, respectively. Both of them were
35
joint events of the Instituto do Milênio with IMPA and the Universidade Federal de Santa
Catarina, respectively, and were much more significant than the previous ones, with strong
international participation, as detailed below.
The contribution of the Instituto do Milênio was essentialfor the above mentioned
meetings, allowing them a better planning of its activities long before the actual event, in
relative freedom from the uncertainties associated to the support from most government
funding agencies. Thanks to this support, these meeting achieved a previously
unreachable level of efficiency and professionalism, which very much contributed to their
unquestionable success.
We summarize next the most relevant data on these workshops. In the 4th workshop
there were 101 registered participants, including 52 foreigners coming from 19 countries
(Argentina, Australia, Austria, Canada, Chile, Cuba, Denmark, France, Germany, Israel,
Japan, Malta, Peru, Poland, Roumania, Russia, Spain, USA and Venezuela).
The most distinguished foreign participants were H. Attouch (U. de Montepelier, France),
A, Auslender (U. de Lyon, France), J. Borwein (Simon Fraser U., Canada), J. Dennis (Rice
U., USA), D. Goldfarb (Columbia U., USA), A. Lewis (Simon Fraser U., Canada), J.
Nocedal (Northwestern U., USA), J.S. Pang (John Hopkins U. USA), K. Shittkowski (U.
Bayreuth, Germany) and A. Shapiro (GeorgiaTech, USA).
In the 5th workshop, honoring C. Gonzaga in his 60th birthday, there were 92 registered
participants, including 31 foreigners from 10 countries (Argentina, Belgium, Canada, Chile,
Colombia, England, France, Mexico, Peru and USA).
The most distinguished foreign participants were F. Alizadeh, (Rutgers U., USA), K.
Anstreicher (U. of Iowa, USA), R. Cominetti (U. de Chile, Chile), D. Goldfarb (Columbia
U., USA), J.L. Goffin (U. de Montreal, Canada), J.S. Pang (Rensselaer I., USA), F. Potra
(U. of Maryland, USA), R. Sargent (Imperial C., England), M. Todd (Cornell U., USA) , L.
Tuncel (U. of Waterloo, Canada) and Y. Ye (U. of Iowa, USA).
The Instituto do Milênio contributed also to the visits of W. Hare (Simon Fraser U.,
Canada) and W. Sosa Sandoval (IMCA, Peru) to IMPA, and of H. Matos (U. de Brasília) to
UFPi.
An important meeting concerning Electrical Energy is being planned within the scope of
the Millenium Institute, under the coordination of Clovis Gonzaga and Yuan Jin Yun, to
take place in the Univ. of Paraná in November, 2004.
Publications 2002-2004
1. Bertolim, M.A., Mello, M.P., Rezende, K.A. Dynamical and topological aspects of
Lyapunov graphs. Qualitative Theory of Dynamical Systems, 5, 57-79, 2004.
2. Birgin, E.G., Martínez, J.M., Ronconi, D. Optimizing the packing of cylinders into a
rectangular container: a nonlinear approach. European Journal on Operations
Research, 160, 19-33, 2004.
3. Bonnans, J.F., Guilbaud, T., Ketfi-Cherif, A., Sagastizábal, C.A., von Wissel, D., Zidani,
H. Parametric optimization of hybrid car engines. Optimization and Engineering, 5,
393-415, 2004.
4. Broda, S., Damas, L., Finger, M., Silva, P.J.S. The decidability of a fragment of BBWlogic. Theoretical Computer Science, 318, 355-372, 2004.
36
5. Daryina, A.N., Izmailov, A.F., Solodov, M.V. Mixed complementarity problems:
regularity, estimates for the distance to a solution, and Newton methods.
Computational Mathematics and Mathematical Physics, 44, 45-61, 2004.
6. Fampa, M.H.C., Maculan, N. Using a conic formulation for finding Steiner minimal tres.
Numerical Algorithms, 25, 315-330, 2004.
7. Gárciga Otero, R., Iusem, A.N. Proximal methods with penalization effects in Banach
spaces. Numerical Functional Analysis and Optimization, 25, 69-91, 2004.
8. Gárciga Otero, R., Svaiter, B.F. A strongly convergent hybrid proximal method in
Banach spaces. Journal of Mathematical Analysis and Applications, 289, 700-711,
2004.
9. Gonzaga, C.C., Cardia. M. Properties of the central points in linear programming
problems. Numerical Algorithms, 35, 185-204, 2004.
10. Graña Drummond, L.M., Iusem, A.N. A projected gradient method for vector
optimization problems. Computational Optimization and Applications, 28, 5-30, 2004.
11. Herskovits, J., Dubeux, V., Araujo, A.L., Mota Soares, C.M. Interior point algorithms for
nonlinearly constrained least square problems. Inverse Problems in Engineering, 12,
211-223, 2004.
12. Herskovits, J., Leontiev, A., Mota Soares, C.M., Huacasi, W. Numerical simulation of
the forest impact on aquifers. Communications on Numerical Methods in Engineering,
20, 585-594, 2004.
13. Herskovits, J., Mappa, P.C., Mota Soares, C.M., Romero, J. Optimal truss design
including plastic collapse constraints. Structural and Multidisciplinary Optimization, 27,
20-26, 2004.
14. Humes Jr, C., Silva, P.J.S., Svaiter, B.F. Some inexact hybrid proximal augmented
Lagrangian algorithms. Numerical Algorithms, 35, 175-184, 2004.
15. Iusem, A.N., Seeger, A. Pointedness, connectedness and convergence results in the
space of closed convex cones. Journal of Convex Analysis, 11, 1-18, 2004.
16. Mascarenhas, W.F. The BFGS algorithm with exact line searchs fails for nonconvex
functions. Mathematical Programming, 99, 49-61, 2004.
17. Mifflin, R. Sagastizábal, C.A. VU-smoothness and proximal point results for some
nonconvex functions. Optimization Methods and Software, 19, 463-478, 2004.
18. Lavor, C.C., Maculan, N. A function to test methods applied to global minimization of
potential energy molecules. Numerical Algorithms, 25, 287-300, 2004.
19. Lopes, V.L.R., Pérez, R.. Recent applications and numerical implementation of quasiNewton methods for solving nonlinear systems of equations. Numerical Algorithms, 35,
261-285, 2004.
20. Makler, S.S., Campelo, M., Saboia, C.H. A computational study of global algorithms for
linear bilevel programming. Numerical Algorithms, 35, 155-173, 2004.
21. Martinhon, C.A.J., Lucena, A.P., Maculan, N. Stronger K-tree relaxation for the vehicle
routing problem. European Journal of Operations Research, 158, 56-71, 2004.
22. Queiroz, M., Humes Jr., C., Judice, J. On finding global optima for the hinge fitting
problem. Computers and Operations Research, 31, 101-122, 2004.
37
23. Queiroz, M., Judice, J., Humes Jr., C. The symmetric eigenvalue complementary
problem. Mathematics of Computation 73, 1849-1863. European Journal of
Operational Research 146, 444-459, 2004.
24. Solodov, M.V. On the sequential quadratically constrained quadratic programming
methods. Mathematics of Operations Research, 29, 64-79, 2004.
25. Solodov, M.V. A class of decomposition methods for convex optimization and
monotone variational inclusions via the hybrid inexact proximal point framework.
Optimization Methods and Software, 19, 557-575, 2004.
26. Andreani, R., Dimitrov, D.K. An extremal non-negative sine polynomial. Rocky
Mountain Journal of Mathematics, 33, 759-774, 2003.
27. Andreani, R., Dunder, C. Martínez, J.M. Order-Value Optimization: formulation and
solution by means of a primal Cauchy method. Mathematical Methods of Operations
Research, 58, 387-399, 2003.
28. Belloni, A, Diniz, A., Maceira, M.E., Sagastizábal, C.A. Bundle relaxation and primal
recovery in unit commitment problems. The Brazilian case. Annals of Operations
Research, 120, 21-44, 2003.
29. Bertolim, M.A., Mello, M.P., Rezende, K.A. Lyapunov graph continuation. Ergodic
Theory and Dynamical Systems, 23, 1-58, 2003.
30. Birgin, E.G. Chambouleyron, I., Martínez, J.M. Optimization problems in the estimation
of parameters of thin films and the elimination of the influence of the substrate. Journal
of Computational and Applied Mathematics, 152, 35-50, 2003.
31. Birgin, E.G., Chambouleyron, I. Martínez, J.M., Ventura, S. Estimation of optical
parameters of very thin films. Applied Numerical Mathematics, 47, 109-119, 2003.
32. Birgin, E.G., Krejic, N., Martínez, J.M. Solution of bounded nonlinear systems of
equations using homotopies with inexact restoration. International Journal of Computer
Mathematics, 80, 211-222, 2003.
33. Birgin, E.G., Krejic, N., Martínez, J.M. Globally convergent inexact quasi-Newton
methods for solving nonlinear systems. Numerical Algorithms, 32, 249-260, 2003.
34. Birgin, E.G., Martínez, J.M., Raydan, M. Inexact spectral projected gradient methods
on convex sets. IMA Journal on Numerical Analysis, 23, 539-559, 2003.
35. Birgin, E.G., Martínez, J.M., Ronconi, D. Minimization subproblems and heuristics for
an applied clustering problem. European Journal of Operations Research, 146, 19-34,
2003.
36. Bonates, T.O.E., Maculan, N. Performance evaluation of a family of criss-cross
algorithms for linear programming. International Transactions in Operations Research,
10, 53-64, 2003.
37. Burachik, R.S., Lopes, J.O. A convergence result for an outer approximation scheme.
Computational and Applied Mathematics, 22, 397-409, 2003.
38. Burachik, R.S., Scheimberg, S., Silva, P.J.S. A Note on the existence of zeroes of
convexly regularized sums of maximal monotone operators. Journal of Mathematical
Analysis and Applications, 280, 313-320, 2003.
39. Burachik, R.S. Svaiter, B.F. Maximal monotonicity, conjugation and the duality product.
Proceedings of the American Mathematical Society, 131, 2379-2383, 2003.
38
40. Butnariu, D., Iusem, A.N., Zalinescu, C. On uniform convexity, total convexity and
convergence of the proximal point and the outer Bregman projection algorithm in
Banach spaces. Journal of Convex Analysis, 10, 35-61, 2003.
41. Dai, H.Y., Martínez, Yuan, J.Y. An increasing-angle property of the conjugate gradient
method and the implementation of large-scale minimization algorithms with line
searches. Numerical Linear Algebra and Applications, 10, 323-334, 2003.
42. Diniz-Ehrhardt, M.A., Gomes-Ruggiero, M.A. Lopes, V.L.R., Martí nez. Discrete
Newton's method with local variations for solving large-scale nonlinear systems.
Optimization, 52, 417-440, 2003.
43. Dostál, Z., Friedlander, A. Santos, S.A. Augmented Lagrangians with adaptive
precision control for quadratic programming with simple bounds and equality
constraints, Siam Journal on Optimization, 13, 1120-1140, 2003.
44. Ferreira-Mendonça, L., Lopes, V.L.R. Pérez, R. Inverse q-columns updating methods
for solving nonlinear systems of equations. Journal of Computational and Applied
Mathematics, 158, 317-337, 2003.
45. Gonzaga, C.C., Castillo, R.A. A nonlinear programming algorithm based on noncoercive penalty functions. Mathematical Programming, 96, 87-101.
46. Gonzaga C.C., Karas E., Vanti, M. A globally convergent filtermethod for nonlinear
programming. SIAM Journal on Optimization, 14, 646-669, 2003.
47. Graña Drummond, L.M., Iusem, A.N. First order conditions for ideal minimization of
vector-valued functions Journal of Convex Analysis, 10, 129-147, 2003.
48. Graña Drummond, L.M., Iusem, A.N. Svaiter, B.F. On first order optimality conditions
for vector optimization. Acta Mathematicae Applicatae Sinica, 19, 371-386, 2003.
49. Herskovits, J., Leontiev, A., Kludhnev, A.M. Nonsmooth domain optimization for elliptic
equations with unilateral costraints. Journal des Mathématiques Pures et Appliquées,
82, 197-212, 2003.
50. Herskovits, J., Pinto Correia, I.F., Mota Soares, C.M., Mota Soares, C.A. Analysis of
adaptive shell structures using a refined laminated model. Compositer Structure, 62,
383-390, 2003.
51. Iusem, A.N. On the convergence properties of the projected gradient method for
convex optimization. Computational and Applied Mathematics, 22, 37-52, 2003.
52. Iusem, A.N., Pennanen, T., Svaiter, B.F. Inexact variants of the proximal point method
without monotonicity. SIAM Journal on Optimization, 13, 1080-1097, 2003.
53. Iusem, A.N., Sosa, W. New existence results for equilibrium problems. Nonlinear
Analysis, 52, 621-635, 2003.
54. Iusem, A.N., Sosa, W. Iterative algorithms for equilibrium problems. Optimization, 52,
301-316, 2003.
55. Izmailov, A.F., Solodov, M.V. Karush-Kuhn-Tucker systems: regularity conditions, error
bounds and a class of Newton-type methods. Mathematical Programming, 95, 631650, 2003.
56. Izmailov, A.I. Solodov, M.V., Chokparov, K.M. Globally convergent algorithms of
Newton type for optimization problems without regularity of constraints. In Problems of
39
Modeling and Analysis in Decision Making Problems (V.A. Bereznev, editor).
Computing Center of the Russian Academy of Sciences, 63-82, 2003.
57. Maculan, N., Passini, M.M., Brito, J.A.M., Loiseau, I. Column generation in integer
linear programming. RAIRO, Recherche Opérationelle, 37, 67-83, 2003.
58. Maculan, N., Santiago, C.P., Macambira, E.M., Jardim, M.H. An O(n) algorithm for
projecting a vector on the intersection of a hyperplane and a box in Rn. Journal of
Optimization Theory and Applications, 117, 553-574, 2003.
59. Martínez, J.M., Martínez, L. Packing optimization for automated generation of complex
system's initial configurations for molecular dynamics and docking. Journal of
Computational Chemistry, 24, 819-825, 2003.
60. Martínez, J.M., Svaiter, B.F. A practical optimality condition without constraint
qualifications for nonlinear programming. Journal of Optimization Theory and
Applications, 118, 117-133, 2003.
61. Mifflin, R. Sagastizábal, C.A. Primal-dual gradient structured functions: second-order
results; links to epi-derivatives and partly smooth functions. SIAM Journal on
Optimization, 13, 1174-1194, 2003.
62. Mifflin, R. Sagastizábal, C.A. On the relation between U-hessians and second-order
epiderivatives. European Journal of Operations Research, 157, 28-38, 2003.
63. Montenegro, F.M.T., Torreão, J., Maculan, N. Microcanonical optimization of the
Euclidean Steiner problem in Rn with applications to phylogenetic inference. Physical
Review E, 68, 2003.
64. Pennanen, T., Svaiter, B.F. Solving monotone inclusions with linear multi-step
methods. Mathematical Programming, 96, 469-487, 2003.
65. Queiroz, M., Humes Jr., C. A heuristic for the continuous capacity and flow
assignment. European Journal of Operational Research, 146, 444-459, 2003.
66. Silva, J.L.C., Soma, N.Y., Maculan, N. A greedy search for the three-dimensional bin
packing problem: the packing static stability case. International Transactions in
Operations Research, 10, 141-153, 2003.
67. Solodov, M.V. Convergence rate analysis of iterative algorithms for solving variational
inequality problems. Mathematical Programming, 96, 513-528, 2003.
68. Solodov, M.V. Merit functions and error bounds for generalized variational inequalities.
Journal of Mathematical Analysis and Applications, 287, 405-414, 2003.
69. Solodov, M.V. On approximations with finite precision in bundle methods for
nonsmooth optimization. Journal of Optimization Theory and Applications, 119, 151165, 2003.
70. Svaiter, B.F. Fixed Points in the family of convex functions representing a maximal
monotone operator. Proceedings of the American Mathematical Society, 131, 38513859, 2003.
71. Chambouleyron, I., Ventura, S., Birgin, E.G., Martínez. Optimal constants and
thickness determination of very thin amorphous semiconductor films. Journal of
Applied Physics, 92, 3093-3102, 2002.
72. Cruz Neto, J.X., Ferreira, O.P., Lucambio Pérez, L. R. Contribution to the study of
monotone vector fields. Acta Mathematica Hungarica, 94, 307-320, 2002.
40
73. Dostál, Z., Friedlander, A. Santos, S.A., Alesawi, K. Augmented Lagrangians with
adaptive precision control for quadratic programming with equality constraints:
corrigendum and addendum. Computational Optimization and Applications, 23, 127133, 2002.
74. Dostál, Z., Friedlander, A., Gomes, F.A.M., Santos, S.A. Preconditioning by projectors
in the solution of contact problems: a parallel implementation. Annals of Operations
Research, 117, 117-129, 2002.
75. Ferreira, O.P., Oliveira, P.R. Proximal point algorithm on riemannian manifolds.
Optimization, 51, 257-270, 2002.
76. Ferreira, O.P., Svaiter, B.F. Kantorovich's theorem on Newton's method in riemannian
manifolds. Journal of Complexity, 18, 304-329, 2002.
77. Garcia, M.V.P., Humes Jr., C., Stern, J.M. Generalized line criterion for Gauss Seidel
method. Journal of Computational and Applied Mathematics, 22, 91-97, 2002.
78. Herskovits, J., Araujo, A.L., Mota Soares, C.M., Pedersen, P. Development of a finite
element method for the identification of material and piezoelectric properties through
gradient optimization and experimental vivration data. Composite Structures, 58, 307318, 2002.
79. Herskovits, J., Leontiev, A., Huacasi, W. An optimization technique for the solution of
the Signorini problem using the boundary element method. International Journal of
Structural Optimization, 24, 72-77, 2002.
80. Herskovits, J., Mota Soares, C.M., Garcia Lage, R.M., Mota Soares, C.A. Development
of a single layer laminated plate finite element model based on Walsh series.
Mechanics of Advanced Materials and Structures, 9, 241-255, 2002.
81. Herskovits, J., Pinto Correia, I.F., Mota Soares, C.M., Mota Soares, C.A. Active control
of axisymmetric shells with piezoelectric layers: a mixed laminated theory with high
order displacements. Computers and Structures, 80, 2265-2275, 2002.
82. Iusem, A.N., Gárciga Otero, R. Augmented Lagrangian methods for cone-constrained
convex optimization in Banach spaces. Journal of Nonlinear and Convex Analysis, 2,
155-176, 2002.
83. Izmailov, A.F., Solodov, M.V. The theory of 2-regularity for mappings with Lipschitzian
derivatives and its applications to optimality conditions. Mathematics of Operations
Research, 27, 614-635, 2002.
84. Izmailov, A.F., Solodov, M.V. Superlinearly convergent algorithms for solving singular
equations and smooth reformulations of complementarity problems. SIAM Journal on
Optimization, 13, 386-405, 2002.
85. Izmailov, A.F., Solodov, M.V. Complementarity constraint qualification via the theory of
2-regularity. SIAM Journal on Optimization, 13, 368-385, 2002.
86. Manssur, L.R.U., Portugal, R., Svaiter, B.F. Group-theoretic approach for symbolic
tensor manipulation. International Journal of Modern Physics C, 14, 859-879, 2002.
87. Martínez, J.M. Minimization of discontinuous cost functions by smoothing. Acta
Applicandae Mathematicae, 71, 245-260, 2002.
88. Mifflin, R. Sagastizábal, C.A. Proximal points are on the fast track. Journal of Convex
Analysis, 9, 563-579, 2002.
41
89. Raupp, F., Gonzaga, C.C. A center cutting plane algorithm for a likelihood estimate
problem. Computational Optimization and Applications, 21, 277-300, 2002.
90. Rey, P.A., Sagastizábal. C.A. Convex normalizations in lift-and-project methods for 0-1
programming. Annals of Operations Research, 116, 91-112, 2002.
91. Rey, P.A., Sagastizábal. C.A. Dynamical adjustment of the prox-parameter in variable
metric bundle methods. Optimization, 51, 423-447, 2002.
92. Sagastizábal, C.A., Solodov, M.V. Parallel variable distribution for constrained
optimization. Computational Optimization and Applications, 22, 111-131, 2002.
93. Birgin, E.G., Martínez, J.M. Large-scale active-set box-constrained optimization
method with spectral projected gradients. Computational Optimization and
Applications, 23, 101-125, 2002.
94. Andreani, R., Friedlander, A. Bound constrained smooth optimization for solving
variational inequalities and related problems. Annals of Operations Research, 116,
p.179-198, 2002.
95. Bahiense, L., Maculan, N., Sagastizábal, C.A. The volume algorithm revisited. Relation
with bundle methods. Mathematical Programming, 94, 41-69, 2002.
96. Solodov, M.V., Svaiter, B.F. A new proximal-based globalization strategy for the
Josephy-Newton method for variational inequalities. Optimization Methods and
Software, 17, 965-983, 2002.
International Journals
1. Andrade, R.C., Lisser, A., Maculan, N., Plateau, G. Telecommunications network
capacity design for uncertain demand. Computational Optimization and Applications.
2. Andreani, R., Birgin, E.G., Martínez, Yuan, J.Y. Spectral projected gradiente and
variable metric methods for optimization with linear inequalities. IMA Journal of
Numerical Analysis.
3. Andreani, R., Gonçalves, P.S., Silva, G.N. Discrete approximations for strict convex
continuous time problems and duality. Computational and Applied Mathematics.
4. Andreani, R.
Friedlander, A., Mello, M.P., Santos, S.A.
Mixed nonlinear
complementarity problems via nonlinear optimization: numerical results on a multi-rigidbody contact problems with friction International Journal of Computational Engineering
Science.
5. Andreani, R., Martínez, J.M., Schuverdt, M.L. The constant positive linear dependence
condition of Qi and Wei implies the quasinormality constraint qualification. Journal of
Optimization Theory and Applications.
6. Bertolim, M.A., Mello, M.P., Rezende, K.A. Poincaré-Hopf
inequalities.Transactions of the American Mathematical Society.
and
Morse
7. Bertolim, M.A., Mello, M.P., Rezende, K.A. Poincaré-Hopf and Morse inequalities for
Lyapunov graphs. Ergodic Theory and Dynamical Systems.
8. Birgin, E.G., Castillo, R., Martínez, J. M. Numerical comparison of augmented
Lagrangian algorithms for nonconvex problems. Computational Optimization and
Applications.
42
9. Birgin, E.G., Raydan, M. Robust stopping criteria for Dykstra's algorithm. SIAM Journal
on Scientific Computing.
10. Bonnel, H., Iusem, A.N., Svaiter, B.F. Proximal methods in vector optimization. SIAM
Journal on Optimization.
11. Bornstein, C.T., Alcoforado, L.F., Maculan, N. A graph orientes approach for the
minimization of the number of late jobs for the parallel machines scheduling. European
Journal of Operations Research.
12. Burachik, R.S., Lopes, J.O., Svaiter, B.F. An outer approximation method for the
variational inequality problem. SIAM Journal on Control and Optimization.
13. Cruz Neto, J.X., Ferreira, O.P., Lucambio Pérez, L.R., Nemeth, S.Z. Convex- and
monotone-transformable mathematical programming problems and a proximal-like
point method. Journal of Global Optimization.
14. Cruz Neto, J.X., Ferreira, O.P., Monteiro, R.D C. Asymptotic behavior of the central
path for SDP problems. Mathematical Programming.
15. Daryina, A.N., Izmailov, A.F., Solodov, M.V.. A class of active-set Newton methods for
mixed complementarity problems. SIAM Journal on Optimization.
16. Diniz-Ehrhardt, M.A. Gomes-Ruggiero, M.A., Martínez, J.M., Santos, S.A. Augmented
Lagrangian algorithms based on the spectral projected gradient for solving nonlinear
programming problems. Journal of Optimization Theory and Applications
17. Ferreira, O.P., Lucambio Pérez, L.R., Nemeth, S.Z. Singularities of monotone vector
fields and extragradient-type algorithm. Journal Of Global Optimization.
18. Gilbert, J-C., Gonzaga, C.C., Karas, E. Examples of ill-behaved central paths in
convex optimization. Mathematical Programming.
19. Gonzaga, C.C., Cardia. M. Using the central path for computing the analytic center of
a polytope. Mathematical Programming.
20. Graña Drummond, L.M., Svaiter, B.F. A steepest descent method for vector
optimization. Journal of Computational and Applied Mathematics.
21. Herskovits, J., Leontiev, A. An interior point technique for solving bilevel programming
problems. Operations Research Letters.
22. Iusem, A.N., Kallio, M. An interior point method for constrained saddle point problems.
Computational and Applied Mathematics\/.
Izmailov, A.F., Solodov, M.V. Newton-type methods for optimization problems without
constraint qualifications. SIAM Journal on Optimization.
23. Martínez, J.M. A note on the theoretical convergence properties of the SIMP method.
Structural and Multidisciplinary Optimization.
24. Martínez, J.M., Pilotta, E.A. Inexact restoration methods for nonlinear programming:
advances and perspectives. In Optimization and Control with Applications (L.Q. Qi,
K.L. Teo and X.Q. Yang, editores). Kluwer.
25. Martínez, J.M. Pilotta, Raydan, M. Spectral gradient methods for linearly constrained
optimization. Journal of Optimization Theory and Applications.
26. Martínez-Legaz, J.E., Svaiter, B.F. Monotone operators representable by lower
semicontinuous convex functions. Set-Valued Analysis.
43
27. Makler, S.S., Campelo, M. A simplex approach for finding local solutions of a linear
bilevel program by equilibrium points. Annals of Operations Research
28. Makler, S.S., Campelo, M. A study of local solutions in linear bilevel programming.
Journal of Optimization Theory and Optimization.
29. Mifflin, R., Sagastizábal, C.A. Relating U-Lagrangians to second order epiderivatives
and proximal tracks. Journal of Convex Analysis.
44
Computer Graphics and Vision
The Millennium Institute IM-AGIMB has greatly contributed to the progress experimented
by this area in the last 3 years or so. Its decisive role permeates the activities that are
presented in the sequel.
Research and Development
In the area of Computer Graphics and Vision, relevant research has been developed in the
following topics, as described in the detailed report: Multiresolution Models; 3D
Photography Immersive Visualization, Video and Multimedia.
There have also been developments related to the following applications: Medical Imaging,
GIS (Geographic Information Systems) and Digital Television.
Educational Track
The educational track resulted in the graduation of 9 master students and 8 PhD students.
These are new researchers that completed their program in the last 30 months.
Emerging Research Centers
The Research Center in Computer Graphics at UFAL has been created under the
coordination of Adelailson Peixoto and with the support of the VISGRAF Laboratory.
Other Educational Activities
Besides the Master and PhD programs, several other educational and scientific activities
have been organized, including the “Workshop of Geometry Processing and Applications”.
New Talents
The researcher Marcelo Bernardes Vieira received the Pro-DOC scholarship from CAPES,
and the student Fabio Dias Morera enrolled in the Master Program in Computer Graphics
at IMPA.
Cooperation with Latin America Mathematical Community
The SIACG – Simpósio Ibero-Americano de Computação Gráfica will take place in
October of 2004, jointly with the SIBGRAPI 2004.
Research Projects
Multiresolution Models
• Volume and Isosurface Models - Vinicius Melo, Luiz Velho (IMPA), and C.Silva
(Oregon Graduate Institue)
• Point Set Models - Jose Luiz Soares, Luiz Velho, and Paulo Cezar Carvalho (IMPA)
• Surface Interpolation Methods - Boris Madrazo, Luiz Velho and Luiz Henrique
Figueiredo (IMPA)
• Multiscale Distance Functions - Antonio Lopes, Claudio Esperanca (UFRJ), and Luiz
Velho (IMPA)
• Surface Parametrization - Afonso Neto, Luiz Velho (IMPA)
• Medial Axis Tranforms - Moacyr Barbosa, Luiz Velho (IMPA), and Ralph Costa (FGV)
45
•
•
•
Morphological Modeling - Ruben Zonenschein, Luiz Velho (IMPA), and Marcelo
Gattass (PUC-Rio)
Learning, Recognition and Synthesis - Anderson Mayrink, Luiz Velho (IMPA) and Davi
Geiger (NYU)
4-K Mesh Construction - Adelailson Peixoto, Luiz Velho (IMPA) and Marcelo Gattass
(PUC-Rio)
3D Photography
• Structured Light Coding - Asla Sá, Vitor Bogado, Luiz Velho and Paulo Cezar Carvalho
(IMPA)
• Visual and Photo Hull Methods - Anselmo, Luiz Velho and Paulo Cezar Carvalho
(IMPA)
• Façade - Jonas, Leandro, Beatriz Alvarez, Luiz Velho and Paulo Cezar Carvalho
(IMPA)
• Match Move - Bruno Madeira, Luiz Velho and Paulo Cezar Carvalho (IMPA)
• Surface Triangulation - Esdras Filho and Luiz Velho (IMPA)
• Object Movies - Aldo Nogueira (UFRJ) and Luiz Velho (IMPA)
• 3D Photography Hardware – Mahtias Zug, Luiz Velho and Roberto Beauclair (IMPA)
Immersive Visualization
• Stereographic Video - Flavio Szenberg (PUC), Luiz Velho and Paulo Cezar Carvalho
(IMPA)
• Motion Tracking - Sergio Biasi, Bruno Feijo (PUC), Luiz Velho and Paulo Cezar
Carvalho (IMPA)
• Storage of 2D Graphical Objects - Sergio Estevao, Luiz Velho (IMPA) and Waldemar
Celes (PUC)
• Super-Resolution - Regis Roblespierre, Stephane Mallat (Ecole Polytecnique), Sérgio
Estevão and Luiz Velho (IMPA)
Video and Multimedia
• Presence - Antonia Lucinelma and Luiz Velho (IMPA)
• Talking Heads - Paula Lucena, Luiz Velho (IMPA), Ken Perlin (NYU), and Bruno Feijo
(PUC)
• Structuring and Tracking - Lourena Rocha, Luiz Velho, and Paulo Cezar Carvalho
(IMPA)
• Smart Capture Station - Matias, Luiz Velho and Roberto Beauclair (IMPA)
• MSRI Mirror – Rosa Ladeira, Luiz Velho, Roberto Beauclair (IMPA)
Applications
Medical Imaging
• Medical Workstation – Aristofanes Correa da Silva and Paulo Cezar Carvalho (IMPA)
• Assisted Interfaces - Marcelo Medeiros, Luiz Velho (IMPA) and Marcelo Gattass (PUC)
Digital Video
• 3D Video – Luiz Velho, Marcelo Bernardes Vieira, Asla Sá and Paulo Cezar Carvalho
(IMPA).
46
GIS
• Interactive Visualization of Very Large Terrain Data Bases – Luiz Velho, Marcelo
Bernardes Vieira, Sergio Estevão, Lourena Rocha (IMPA).
Scientific Publications 2002-2004
1. Yaohua Hu, Luiz Velho, Xin Tong, Baining Guo, and Harry Shum. Realistic, Real-Time
Rendering of Ocean Waves. Computer Animation and Virtual Worlds. Special Issue on
Game Technologies, 2004.
2. Luiz Velho, A Dynamic Adaptive Mesh Library Based on Stellar Operators.
Journal of Graphics Tools, 9(2), 1-29, 2004.
3. Luiz Henrique Figueiredo, Jorge Solfi, and Luiz Velho. Approximating Parametric
Curves with Strip Trees using Affine Arithmetic. Computer Graphics Forum, 22(2), 171180, June 2003.
4. Jingdan Zhang, Kun Zhou, Luiz Velho, Baining Guo, and Heung-Yeung. Synthesis of
Progressively Variant Textures on Arbitrary Surfaces. ACM Transactions on Graphics,
22(3), 295-302, July 2003.
5. Asla Medeiros e Sá, Esdras Soares de Medeiros Filho, Paulo Cezar Carvalho, and
Luiz Velho. Coded Structured Light for 3D-Photography: an Overview. RITA - Revista
de Informatica Teorica e Aplicada, 2002.
6. Jonas Gomes and Luiz Velho, Color Representation: Theory and Techniques.
Cubo Matematica Educacional, 4(2), June 2002.
7. Paula Salgado Lucena, Marcelo Gattass, and Luiz Velho. Expressive Talking Heads: A
Study on Speech and Facial Expression in Virtual Characters, Revista SCIENTIA,
2002.
8. Luiz Velho and Ken Perlin, B-Spline Wavelet Paint, Revista de Informática Teórica e
Aplicada, 2002.
9. Luiz Velho, Ken Perlin, Henning Biermann, and Lexing Ying. Algorithmic Shape
Modeling with Subdivision Surfaces.
Books
1. Jonas Gomes
IMPA, 2003.
and
Luiz
Velho,
Fundamentos
da
Computação
Gráfica.
2. Luiz Velho and Paulo Cezar Carvalho, Mathematical Optimization in Graphics and
Vision. ACM SIGGRAPH. Course Notes, 2003.
3. Luiz Velho and Paulo Cezar Carvalho, Mathematical Optimization Methods in
Graphics and Vision. SIGGRAPH 2002 Course Notes, SIGGRAPH-ACM, San Antonio,
Texas, July 2002.
4. Luiz Velho, Jonas Gomes, and Luiz Henrique Figueiredo. Implicit Objects in Computer
Graphics. Springer Verlag, New York, 2002.
47
Chapters in books
1. Adelailson Peixoto and Luiz Velho. Adaptive Mesh Extraction using Simplification and
Refinement. pages 325-334. Curve and Surface Design: Saint-Malo. Nashboro Press,
2003.
2. Vinicius Mello, Luiz Velho, Paulo Roma Cavalcanti, and Claudio Silva. A Generic
Programming Approach to Multiresolution Spatial Decompositions, volume
Visualization and Mathematics III. Springer Verlag, 2002.
Papers Published in Conferences Proceedings
1. Paula Lucena Rodrigues, Bruno Feijó, and Luiz Velho. Expressive Talking Heads:
uma ferramenta de animação com fala e expressão facial sincronizadas para o
desenvolvimento de aplica c cões interativas. In Proceedings of Webmídia. SBC,
2004.
2. Rogério Ferreira Rodrigues, Paula Salgado Lucena Rodrigues, Bruno Feijó, Luiz
Velho, and Luiz Fernando Gomes Soares. Cross-Media and Elastic Time Adaptive
Presentations: the Integration of a Talking Head Tool into a Hypermedia Formatter.
In Proceedings of Adaptive Hypermedia. ACM SIGART, 2004.
3. Adelailson Peixoto, Marcelo Gattass, and Luiz Velho. Extração de malhas adaptativas
com operações de simplificação e refinamento. In XVI Concurso de Teses e
Dissertações, Sociedade Brasileira de Computação, 2003.
4. Aldo Nogueira, Elaine Prata, and Luiz Velho. Visualização de Objetos Tridimensionais
Baseada em Interpolação Projetiva. In Proceedings of I Workshop de Trabalhos de
Iniciação Científica em Computação Gráfica e Processamento de Imagens, 2003.
WICCGPI'2003.
5. Asla Sa and Luiz Velho Paulo Cezar Carvalho. Recovering Registered Geometry and
High Dynamic Range Texture with Coded Structured Light. In Proceedings of The 11th
International Conference in Central Europe on Computer Graphics, Visualization and
Computer Vision, 2003.
6. Boris Mederos, Luiz Velho, and Luiz Henrique de Figueiredo. Moving Least Squares
Multiresolution Surface Approximation. In Proceedings of SIBGRAPI 2003, XVI
Brazilian Symposium on Computer Graphics and Image Processing. IEEE Press,
2003.
7. Esdras Medeiros, Luiz Velho, and Helio Lopes. A Topological Framework for
Advancing Front Triangulation. In Proceedings of SIBGRAPI 2003, XVI Brazilian
Symposium on Computer Graphics and Image Processing, 2003.
8. Luis Rivera, Luiz Velho, and Paulo Cezar Carvalho. Oriented Bounding Boxes Based
on Multi-resolution Contours. In Anais do Primeiro Congreso Internacional De
Científicos Peruanos, 2003.
9. Luiz Velho. Stellar Subdivision Grammars. In Proccedings of Eurographics
Symposium on Geometry Processing, 2003.
48
10. Paula Lucena, Marcelo Gattass, and Luiz Velho. Expressive Talking Heads: Um
Estudo de Fala e Expressão Facial em Personagens Virtuais. In XVI Concurso de
Teses e Dissertações, Sociedade Brasileira de Computação, 2003.
11. Paula Lucena Rodrigues, Bruno Feijó, and Luiz Velho. Expressive Talking Heads:
uma ferramenta de animação com fala e expressão facial sincronizadas para o
desenvolvimento de aplicações interativas. In Proceedings of Webmidia, 2003.
12. Vinicius Mello, Luiz Velho, and Gabriel Taubin. Computing the In/Out function of Point
Clouds. In Proceedings of the 8th ACM Symposium on Solid Modeling and
Applications, 2003.
13. Wilson Vieira, Helio Lopes, Geovan Tavares, Thomas Lewiner, and Luiz Velho. Fast
Stellar Mesh Simplification. In Proceedings of SIBGRAPI 2003, XVI Brazilian
Symposium on Computer Graphics and Image Processing. IEEE Press, 2003.
14. Anderson Cunha, Ralph Teixeira, and Luiz Velho. Discrete Scale Spaces.
In Proceedings of the International Symposium on Mathematical Morphology, VI.
CSIRO Mathematical and Information Sciences, April 2002.
15. Andre Parente, Luiz Velho, and Sergio Pinheiro. O Visorama. In Proceedings do I
Workshop de Realidade Virtual e Visualizacao Cientifica, 2002.
16. Antonia Lucinelma Pessoa Albuquerque and Luiz Velho. Togetherness through Virtual
Worlds: How real can be that Presence? Editor Universidade Fernando Pessoa, Fifth
Annual International Workshop Presence, ISBN: 9728184-88-3, p.435-447, Porto,
Portugal, October 2002.
17. Antonio Apolinario Jr., Claudio Esperanca, and Luiz Velho. A Representation of
Implicit Objects Based on Multiscale Euclidean Distance Fields. In Proceedings of
SIACG 2002 - First Ibero-American Symposium on Computer Graphics, p.119-129,
Guimaraes, July 2002. Eurographics Portuguese Chapter.
18. Asla Sa, Paulo Cezar Carvalho, and Luiz Velho. (b, s)-BCSL : Structured Light Color
Boundary Coding for 3D Photography. In Proceedings of 7th International Fall
Workshop on Vision, Modeling, and Visualization, 2002.
19. Diego Nehab and Luiz Velho. Multiscale Moment-Based Painterly Rendering.
In Proceedings of SIBGRAPI 2002, XV Brazilian Symposium on Computer Graphics
and Image Processing, Fortaleza, October 2002. SBC, Sociedade Brasileira de
Computacao, IEEE Press.
20. Lourena Rocha, Luiz Velho, and Paulo Cezar Carvalho. Image Moments-Based
Structuring and Tracking of Objects. In Proceedings of SIBGRAPI 2002 - XV Brazilian
Symposium on Computer Graphics and Image Processing. SBC, Sociedade Brasileira
de Computacao, IEEE Press, October 2002.
21. Luiz Velho and Jonas Gomes. Color Halftoning with Stochastic Dithering and Adaptive
Clustering. In Proceedings of the First European Conference on Color in Graphics,
Image and Vision. Society for Imaging Science and Technology, 2002.
49
22. Luiz Antonio Rivera, Paulo Cezar Carvalho, and Luiz Velho. Oriented Bounding Boxes
Based on Multi-resolution Contours. In Anais do Primeiro Congresso Internacional de
Cientificos Peruanos, 2002.
23. Luiz Henrique de Figueiredo, Jorge Stolfi, and Luiz Velho. Approximating Parametric
Curves with Strip Trees using Affine Arithmetic. In Proceedings of SIBGRAPI 2002, XV
Brazilian Symposium on Computer Graphics and Image Processing, Fortaleza,
October 2002. SBC, Sociedade Brasileira de Computacao, IEEE Press.
24. Sergio Pinheiro and Luiz Velho. A virtual memory system for real-time visualization of
multi-resolution 2D objects. In Proceendings of WSCG, 2002.
Degrees Awarded 2002-2004
M.Scs. Theses
Antonio Wilson Vieira. Uma Abordagem Topológica para Simplificação de Malhas, PUC,
Advisor: Helio Lopes
Danilo Tuller. Abstração de Alto Nível para Programação do Processador Gráfico,
PUC-Rio, Advisor: Waldemar Celes
Esdras Medeiros Filho. Algoritmo Ball-Pivoting: Contextualização e Estado da Arte. IMPA,
August 2003, Advisor: Luiz Velho
Francisco Petrucio Cavalcante Junior. Rasterização de Curvas Implícitas Usando
Aproximações de Distância, IMPA, Advisor: Luiz Henrique Figueiredo
Heloisa Reis Leal. Operações Booleanas na Modelagem por Pontos. PUC-Rio. Advisor:
Luiz Velho and Waldemar Celes
Juliano Camargo. Alinhamento por Maximização de Informação Mútua, IMPA, Advisor:
Paulo Cezar Carvalho
Paula Salgado Lucena. Expressive Talking Heads - Um Estudo de Fala e Expressão em
Personagens Virtuais. PUC-Rio, June 2002. Advisor: Luiz Velho (co-advisor: Marcelo
Gattass)
Romaric Audigier. Segmentacao Interativa, UNICAMP, Advisor: Roberto Lotufo.
Thomas Lewiner. Constructing Discrete Morse Functions, PUC-Rio. Advisor: Helio Lopes
Ph.Ds. Theses
1. Adelailson Peixoto da Silva. Extração de Malhas Adaptativas em Multi-resolução a
partir de Volumes usando Simplificação e Refinamento. PUC-Rio, October 2002.
Advisor: Marcelo Gattass and Luiz Velho.
2. Anselmo Montenegro. Reconstrucao de Cenas a partir de Imagens, PUC, Advisor:
Paulo Cezar Carvalho and Marcelo Gattass.
3. Aristofanes Correa Silva. Algoritmos para Diagnóstico Assistido de Nódulos
Pulmonares Solitários em Imagens de Tomografia Computadorizada, PUC-Rio,
January 2004. Advisor: Marcelo Gattass and Paulo Cezar Pinto Carvalho.
50
4. Boris Mederos Madrazo. Surface Reconstruction from Noisy Point Clouds,
Advisor: Luiz Velho and Luiz Henrique Figueiredo.
IMPA.
5. Luciano Silva, Pertinência em Dimensão Arbitrária com Multiresolução, IME-USP.
Advisor: Elias Fabris.
6. Marcelo Bernardes Vieira. Inferencia de Orientação de Dados Esparsos para
Reconstrução de Superfícies, UFMG, Advisor: Arnaldo Albuquerque.
7. Marcelo Medeiros Carneiro. Interfaces Assistidas para Deficientes Visuais Utilizando
Dispositivos Reativos e Transformadas de Distância, PUC-Rio, April 2003. Advisor:
Luiz Velho and Marcelo Gattass.
8. Sergio Estevao Machado Lisboa Pinheiro. Um sistema de cache preditivo para o
processamento em tempo-real de grandes volumes de dados gráficos.
PhD thesis, PUC-Rio, February 2004. Advisor: Luiz Velho and Waldemar Celes.
Conferences Organized
Workshop of Geometry Processing and Applications IMPA-PUC-Rio. September 14-16.
Organizers: Luiz Velho and Geovan Tavares
Invited Speakers:
•
•
•
•
•
•
•
•
Nina Amenta
Marshall Bern
Luiz Henrique Figueiredo
Helio Lopes
Jorge Stolfi
Claudio Esperanca
Luiz Gustavo Nonato
Thomas Lewiner
6. Research Visitors
Jonathan Shewchuck, UCLA 01 a 11 de Setembro de 2003
Nina Amenta, USC – 12 a 19 de Setembro de 2004
7. Post-Doctoral Scholarship
Adelailson Peixoto – Outubro 2003
51
PART I – Biological systems
1.
2.
3.
4.
Conceptual summary of the advances during the last 30 months.
List of publications during the last 30 months.
List of completed doctorates during the last 30 months.
How did the Millennium Institute contribute to the results and in the preparation of
researchers?
5. The impact of the Millennium Institute in research activities such as workshops,
meetings, and research exchanges.
6. Plans for future activities.
PART II – Stochastic modeling in linguistic
1.
2.
3.
4.
5.
6.
Introduction
Conceptual achievements in the are in the last 30 months.
Scientific Production
Nurturing of human resources in the period
Contribution by the IM-AGIMB
Plans for the Future
PART I
Conceptual summary of the advances in the last 30 months
We start by remarking that an effective interaction between mathematical sciences
researchers and their biophysical and biological counterparts is still in a very incipient
period in our country. Added to that we have the fact that it is very hard to find and to form
researchers with solid knowledge in both the biosciences and in the mathematical
sciences. In this context, the IM - AGIMB substantially contributed to the advance of the
interdisciplinary efforts through biomath workshops, seminars, and courses. The effect of
such contribution, however, will become even evident in the next few years when students
and young researcher that participated in the several events will start to develop research
in the field.
On a conceptual level, we note the following developments:
•
Modeling of respiratory tract and function by means of mathematical techniques by the
group of Walter Zin.
•
Symmetries of the genetic code and finite groups. Preservation. Symmetry
preservation in the evolution of the genetic code, by M. Forger, J.E. Hornos and their
groups.
•
Diffusion of new techniques in epidemiology and virus dynamics, specially the quasispecies equations and evolutionary dynamics (Nowak, May, Sigmund). A project that
has benefited from such visits is the doctoral dissertation of Dayse Haime Pastore.
52
•
Scaling limit techniques of kinetical models (Boltzmann type equations) started to be
used in an effective way to treat certain chemotaxis models. This work has been
developed jointly between Fabio Chalub, Peter Markowich and Benoit Perthame.
•
New efficient algorithms based on tridimensional tomographic techniques to tackle the
transmission microscopy problem. Such algorithms were directed towards applications
to macromolecules imaging. This is work that was developed by J. P. Zubelli, jointly
with the group of G. T. Hermann (CUNY).
•
Fractals in biology by Luiz Bevilacqua.
•
Advances in the study of flagellated organism mobility using techniques from geometric
mechanics. Jair Koiller is developing this work in collaboration with Om Kurt Ehlers,
Greg Huber, e Gerusa A. Araujo.
Publications
1. Antoneli, F., Forger, M. and Hornos, J.E., The search for symmetries in the genetic
code: finite groups, Modern Physics Letters B, March, 2004.
2. Araújo, G. and Koiller, J., Self-Propulsion of N-Hinged 'Animats' at Low Reynolds
Number, Qualitative theory of dynamical systems, 5, 15-43, 2004.
3. Chalub, F., Schmeiser, C., Perthame, B. and Markowich, P., Kinetic Models for
Chemotaxis and Their Drift-Diffusion Limits. Monatshefete Für Mathematik, 142(1-2),
123-141, 2004.
4. Hornos, J.E.; F, Braggion, L., Magini, M. and Forger, M., Symmetry preservation in the
evolution of the genetic code, Life, 56 (3), 125-130, March, 2004.
5. Lucangelo, U., Antonaglia, V., Zin, W.A., Fontanesi, L., Peratoner, A., Bird, F.M. and
Gullo, A. Effects of mechanical load on flow, volume and pressure delivered by highfrequency percussive ventilation. Respir. Physiol. Neurobiol. (no prelo).
6. Antoneli, F., Braggion, L., Forger, M. and Hornos, J.E., Extending the search for
symmetries in the genetic code, Internat. J. Modern Phys., B 17(17), 3135-3204, 2003.
7. Frid, H., Jabin, P.E. and Perthame, B., Global stability of steady solutions for a model
in virus dynamics. M2AN-Mathematical Modelling and Numerical Analysis, 37(4), 709723, 2003.
8. Locchi, F., Chelucci, G.L. and Zin, W.A., Determination of rate-constants as a method
to describe passive expiration. Eur. J. Appl. Physiol. 90, 539-548, 2003.
9. Zubelli, J.P., Marabini, R. Sorzano, C.O.S. and Herman, G.T., Three-Dimensional
Reconstruction by Chahine's Method from Electron Microscopic Projections Corrupted
by Instrumental Aberrations, Inverse Problems, 19(4), 933-950, 2003.
Ph.Ds. Theses
1. Fabio A.C.C. Chalub – Supervisor: Jorge Zubelli
2. Fernando Martins Antoneli – Supervisor: Michael Forger
3. Gerusa A. Araujo – Supervisor: Jair Koiller
53
How did the Millennium Institute contribute to the results and in the preparation of
researchers?
During the last two Summer Sessions at IMPA we promoted activities in biomathematics.
We also sponsored minicourses on biophysical modelling and game theory. These
activities certainly impacted on the development of the doctoral dissertation of Gerusa A.
Araujo and Dayse Haime Pastore, as well as in the master's thesis of Ana Maria Luz
entitled "Modelos Difusivos e Cinéticos para Quimiotaxia"
(http://www.preprint.impa.br/Shadows/SERIE B/2004/7.html) under Prof. Jorge P. Zubelli.
We brought a large number of researchers from Brazil and abroad. To cite a few:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
J. Hofbauer (Vienna)
Michael Turelli (UCD)
Karl Sigmund (Vienna)
Peter Markowich (Vienna)
Martin Nowak (Harvard)
Franziska Michor (Harvard)
Christoph Hauert (UBC)
Larry Liebovitch (F.A.U.)
Greg Huber (UMB)
Marcelo Magnasco (Rockefeller Univ.)
We also developed research exchanges with the folowing groups:
1. Paulo Murilo Oliveira (UFF)
2. Claudio Struchiner (Fiocruz/RJ)
3. Jose Fontanari, Michael Forger, Eduardo Massad, Coraci Malta, Joyce Bevilacqua
(USP)
4. Hyun Yang (UNICAMP)
5. Rita Zorzenon (UFPE)
6. Rita de Almeida (UFGRS)
Plans for future activities:
New courses. Besides the traditional course in Molecular Sciences at USP-SP,
coordinated by Prof. Regina Markus (http://www.cecm.usp.br/index.html), new B.Sc.
Courses combining exact and life sciences are being created in IBCCF-RJ. A new M.Sc.
course on Biomathematics is being planned at Fiocruz-RJ. Research Institutes, such as
IMPA and LNCC, have been stimulating doctoral theses in biological themes.
An induced program We think that a coordinated planning of activities could be studied,
say, by a Committee from ABC (Brazilian Academy of Sciences), and/or leading to an
induced CNPq program. Due to its interdisciplinarity, it is necessary the combination of
biomathematics, bioengineering, biophysics and biochemistry. Note the the last two have
old and strong Scientific Societies in Brazil, that meet annually at FESBE. From the side
of the Exact Sciences, there is a traditional initiative of Biomathematics sections at
SBMAC meeting http://www.sbmac.org.br, in recent years coordinated by J. Bevilacqua
and C. Malta ("outreach representative" in Brazil of the Society for Mathematical Biology,
see http://www.smb.org/)
54
New opportunities in Biomathematics. In the last tem years the modeling of intracellular phenomena exploded, specially the molecular motors. One can predict that 21
century will not only witness the expansion of the methods of Mathematical Physics to the
biological realm, from the reductionist viewpoint, but also the methods of Control and
Optimization, from the global or "anti-reducionist" point of view. For further information see
•
•
http://www.sciencemag.org/sciext/mathbio/
www.ams.org/notices/200403/comm-reed.pdf
IM-AGIMB shall focus its efforts in these new opportunities, and we call attention to the
initial important activities of the optical tweezers group at UFRJ, coordinated by Moyses
Nussenzweig and Vivaldo Moura Neto.
PART II
Stochastic Modeling in Linguistics
Introduction
Senior researchers in the Brazilian team:
Antonio Galves, IME-USP
Charlotte Galves, IEL-UNICAMP
Nancy Lopes Garcia, IMECC-UNICAMP
Arnaldo Mandel, IME-USP
Claudia Peixoto, IME-USP
Junior researchers related to the project:
Miguel Abadi, IMECC-UNICAMP
Denise Duarte, Matemática-UFG
Davide Gabrielli, Matematica-L’Aquila
Jesus Garcia, IMECC-UNICAMP
Main international collaborators:
Marzio Cassandro, Fisica-Roma La Sapienza
Pierre Collet, CNRS/École Polytechnique
Emmanuel Dupoux, Sciences Cognitives-ENS
Roberto Fernández, Mathématiques-Rouen
Ricardo Fraiman, Matemática-San Andrés
Anthony Kroch, Linguistics-UPenn
The primary goal of the activities of this group is the construction of a mathematical model
for the relationship between syntax and prosody in child language acquisition and its
consequences on the linguistic change in time. The linguistic theory in its present form is
unable to treat this question. Our solution is provided by Probability Theory and
Thermodynamical Formalism. From this point of view, the linguistic production is modeled
as a Gibbs state associating probabilities to sequences of lexical items, syntax and
phonological domain boundaries. In this model, the syntax is represented as a set of
restrictions over the admissible sequences of symbols. The prosody is represented as a
thermodynamical potential. These ideas were initially presented in the following papers:
Maximum likelihood and minimum entropy identification of grammars (Collet, Galves and
Lopes 1995), A Statistical-Physics approach to language acquisition and language change
55
(Cassandro, Collet, Galves and Galves 1999) e Identifying features in the presence of
competing evidence, the case of first language acquisition, (Fernández and Galves 2000).
As we shall describe later, IM-AGIMB played a key role to the progress in this area in the
last 30 months.
Conceptual achievement in the area in the last 30 months
A summarized list of the results follows.
Probabilistic methodology developed in order to study linguistic chains
1. Collet, Duarte and Galves, A new bootstrap method and central limit theorem for
bootstrap estimators for cylindrical functions, 2004.
2. Cassandro, Collet, Duarte, Galves and Garcia, Introduction of the notion of connected
families of quantified chains and estimation of cut-off points, 2004
3. Cuesta-Alberto, Fraiman, Galves, Garcia and Svarc, Kolmogorov-Smirnov tests for the
sonority of speech and identification of rhythmic classes, 2004.
4. Abadi and Galves; Gabrielli, Galves and Guiol, Entropy estimation in symbolic chains
of infinite order, 2003.
5. Fernández and Galves, Markov approximations for chains of infinite order, 2002.
Linguistic-probabilistic Modeling
1. Introduction of the notion of speech sonority and its application to the identification of
rhythmic classes of natural languages (Galves, Duarte, Garcia and Galves 2002)
2. Mathematical modeling of rhythmic patterns in language (Abaurre, Galves, Mandel and
Sândalo 2004; Galves, Galves, Garcia and Peixoto 2004)
3. Identification of anomalous sequences in linguistic and biological chains (Abadi 2004)
Modeling the interface syntax/phonology using optimality theory (Abaurre, Galves,
Mandel and Sândalo 2004; Galves and Sândalo 2004)
A measure of the impact of our research inside the field of Linguistic is the choice of the
paper "Sonority as a basis for rhythmic class discrimination" (Galves, Garcia, Duarte e
Galves, 2002) by a panel of referees as one of the four to be presented in a plenary
session of perhaps the most prestigious meeting in 2002, Speech Prosody 2002, held in
Aix-en-Provence.
Next, we briefly present the conceptual framework in which our research has developed. A
central question for the construction of the mathematical model of he syntax/phonology
interaction is the characterization of the thermodynamical potential describing the
language prosody. The statistical analysis of the phonetic data which are relevant for the
identification of the features of this potential, and the development of the statistical theory
necessary for the analysis is the main goal of the team at this moment.
56
Following the track suggested by recent research initiated by Ramus, Nespor e Mehler
(1999), our work has been guided by the notion of acoustic correlates of rhythm. In this
direction, we proposed a new sonority measure as a basis to discriminate rhythmic
classes. This approach is presented in "Sonority as a basis for rhythmic class
discrimination" (Galves, Garcia, Duarte e Galves, 2002). There are empirical evidences
that for each language the sonority can be well modeled as a quantified chain with two
adjacent states. These chains have the following characteristic: the discrete chains which
are underlying the sonority have distributions which differ from language to language.
However, the two distributions corresponding to the two adjacent states are universal. This
allows us first to statistically identify the cut-off point that separates the two sonority
regions and next to codify the sonority using a chain of infinite order assuming two values.
All the rhythmic information for each language would be carried by these chains. The
statistical methodology to carry out this program is currently being constructed. The first
results are presented in Denise Duarte´s Ph.D. Thesis "Aproximações markovianas e
reamostragem em cadeias de ordem infinita com aplicação à linguística", (2003) and in
the papers cited in item 1.
Besides the work with the acoustic speech signal we are searching for the existence of the
fingerprints of rhythm in written texts. The paper “The Sotaq optimality based computer
program and secondary stress in two varieties of Portuguese” (Abaurre, Galves, Mandel e
Sândalo 2004) provides evidence that Modern European Portuguese (EP) and Brazilian
Portuguese (BP) construct rhythmic units differently. This suggests that the stochastic
process formed by the successive words in a text, codified according to the position of
their main stresses, number of syllables, boundaries of the prosodic words, have distinct
laws. More precisely, assuming that this process comes from a variable length Markov
chain, we find that the context functions corresponding to EP and BP are different: only in
EP the process forgets the past when it finds a stress. This work is presented in
“Correlates of rhythm in written texts of Brazilian and Modern European Portuguese”
(Galves, Galves, Garcia and Peixoto 2004, in progress).
Scientific production 2002-2004
Published or accepted papers
1. Abadi, M. and A. Galves, A version of Maurer's conjecture for psi-mixing processes,
Nonlinearity 17(4), 1357-1366, 2004.
2. Abaurre, M.B.M, C. Galves, A. Mandel, and F. Sandalo, The Sotaq optimality based
computer program and secondary stress in two varieties of Portuguese, Probus, 2005.
3. Dias, R and N.L. Garcia, A spline approach to nonparametric testing of hypotheses,
Braz. Journal of Prob. and Stat., 2004.
4. Galves, C and M.F. Sandalo, Clitic-placement in European Portuguese and the
Syntax-Phonology Interface, MIT Working Papers in Linguistics, 44, 2004.
5. Galves, A., D. Gabrielli and D. Guiol, Fluctuations of the empirical entropies of a chain
of infinite order, Math. Phys. Electron. J., 9/5(5), p.9, 2003.
6. Britto, H., M.Finger and C. Galves, Computational and linguistic aspects of the
construction of The Tycho Brahe Parsed Corpus of Historical Portuguese, In Pusch,
Claus D., Raible, Wolfgang (eds.), Romanistische Korpuslinguistik, Korpora und
57
gesprochene Sprache, Romance Corpus Linguistics, Corpora and Spoken Language,
ScriptOralia, 126. Tübingen: Narr., 2002.
7. Fernández, R. and A. Galves, Markov Approximations of Chains of infinite order,
Bulletin Brazilian Mathematical Society, New Series, 33(3), Springer, 295-306, 2002.
8. Galves, A., D. Duarte, J. Garcia and C. Galves, Sonority as a basis for rhythmic class
discrimination, Speech Prosody 2002, Proceedings of the first International
Conference on Speech Prosody, Laboratoire Parole et Langage, Aix-en-Provence,
323-326, 2002.
9. Garcia, J, U. Gut and A. Galves, Vocale, a semi-automatic tool for prosodic research,
Speech Prosody 2002, Proceedings of the first International Conference on Speech
Prosody, Laboratoire Parole et Langage, Aix-en-Provence, 2002.
Submitted or working papers
1. Abadi, M. Poisson approximations and identification of rare strings in biological chains,
working paper, 2004
2. Cassandro, M., P. Collet, D.Duarte, A. Galves and J. Garcia. A stochastic model for
the speech sonority: tied quantized chains and cross-linguistic estimation of the cutpoints, working paper, 2004.
3. Collet, P., D. Duarte and A. Galves. Bootstrap central limit theorem for chains of
infinite order via Markov approximations, 2004. Submitted
4. Cuesta-Alberto, J., R. Fraiman, A. Galves, J. Garcia and M. Svarc. Identifying rhythmic
classes through the sonority of languages: a Kolmogorov-Smirnov approach, working
paper, 2004.
5. Galves, A., C. Galves, N. Garcia and C. Peixoto. Correlates of rhythm in written texts
of Brazilian and Modern European Portuguese, working paper, 2004.
http://www.ime.usp.br/~galves/artigos/boot.pdf
Electronic Corpus and computational tools developed by the project team:
•
The parsed Corpus of Historical Portuguese Tycho Brahe: electronic set of texts
written by Portuguese authors born between 16th and 19th centuries, annotated and
freely available to the community at the site http://www.ime.usp.br/~tycho/corpus. The
Tycho Brahe Corpus has at this moment 1.851.619 words, including 1.019.191 words
in a morphological labeled version. The construction of this corpus required the
construction of computational tools for annotation (cf. Britto, Finger and Galves 2002).
The posterior development of these tools is a very promising area for probabilistic and
computational research.
•
Piccolo e Vocale: These are two computational tools for the treatment of the acoustic
speech signal which were developed by the project team. Piccolo computes the
sonority in the signal and Vocale segments the signal into consonantal and vocalic
intervals (cf. Garcia, Gut and Galves 2002). Both are freely available to the academic
community at (http://ww.ime.usp.br/~tycho/prosody/).
58
Nurturing of human resources in the period
Ph.D. Theses
•
Daniela Guiol. Comportamento assintótico de estimadores da entropia para cadeias
de ordem infinita com perda de memória exponencial. IME-USP, advisors Antonio
Galves e Nancy Lopes Garcia.
•
Denise Duarte. Aproximações markovianas e reamostragem para cadeias de ordem
infinita com aplicação à lingüística. IME-USP, advisor Antonio Galves.
Post-Doctoral
•
•
•
•
Anne Cros, IME-USP, advisor Antonio Galves.
Davide Gabrielli, IME-USP, advisor Antonio Galves.
Jesus Garcia, IME-USP, advisor Antonio Galves.
Miguel Abadi, IME-USP, advisor Pablo Ferrari.
Contribution of the Millennium Institute
IM-AGIMB was instrumental to the development of research in the area and the nurturing
of human resources.
Promotion of visits by foreign participants in the research projects:
•
•
•
•
Davide Gabrielli, November, 2003
Marzio Cassandro, November, 2003
Olivier Bertoncini (Rouen), July/August, 2004
Roberto Fernández, June, 2004
Promotion of meetings
•
Workshop on Probabilistic Phonology, coord. Antonio Galves, Barra do Sahy, 30/Oct.1/Nov, 2003
•
Oficina de modelização estocástica em Lingüística, coord. Antonio Galves, 1er
Encuentro Regional de Probabilidad y Estadística Matemática, Buenos Aires,
30/Sept. – 2/Oct., 2004
Plans for the future
Development of the following research projects:
•
Comportamento estocástico, fenômenos críticos e identificação de padrões rítmicos
nas línguas naturais, Projeto Temático PRONEX/Fapesp.
Cf. http://www.ime.usp.br/~tycho/what.
•
Padrões rítmicos, fixação de parâmetros e mudança lingüística, fase II, Cf.
http://www.ime.usp.br/~tycho/what
59
The contribution of the Millennium Institute, IM-AGIMB to the progress of mathematical
research has been of fundamental importance. This was done by sponsoring activities of
the highest quality and giving support to the planning and execution of the different
activities. In fact, the promotion of IM-AGIMB to the advancement of Geometry took that
area of research to a new level of quality. The existence of the Institute represents a huge
progress in order to keep the mathematical research in Brazil at the best international
level.
Advances reached in the period
The advancement of mathematical research during the last 30 month can be described by
the following two fundamental aspects:
(a) Strong progress on those subjects where research in Geometry was already strong,
namely, Submanifold geometry, Differential equations and submanifolds in Riemannian
manifolds, the interaction between Geometry and Mathematical-Physics, subRiemannian and semi-Riemannian geometry, Lie groups, Minimal surfaces, Surfaces
of constant mean curvature and recent extensions, namely, Submanifolds with
constant r-mean curvature. In several cases, advances were due to the use of
sophisticated mathematical tools from Analysis, Partial differential equations theory
and Topology.
(b) New subjects of research like Geometric Analysis, Partial differential equations and Lie
Groups.
(c) (a) is clear just by checking the papers published by the group of geometers in the
country. Item (b) is a natural consequence of the arrival of several young
mathematicians who got theirs PH D's abroad at first class universities.
One could see during the several meetings being held during the period a strong
interaction between researchers with different background and objectives. The large
number of participants consisting of students, professors and visitors has significantly
increased in quantity and quality in research.
1. Borrelli, Gorodsky, C., Minimal Legendrian submanifolds and absolutely areaminimizing cones, Diff. Geom and Applic, 2004.
2. Do Carmo, M. P., Elbert, M. F., On stable complete hypersurfaces with vanishing rmean curvature. Tohuku Mathematical J., 1-10, 2004.
3. Do Carmo, M. P., Xia, C., Complete manifolds with nonnegative Ricci curvature and
the Caffarelli-Kohn-Niremberg inequalities, Compositio Math. Dordrecht, 140, 818-826,
2004.
4. Gorodsky, C. Olmos and R. Tojeiro, Copolarity of isometric actions, Trans. Amer.
Math. Soc, 356, 1585-1608, 2004.
60
5. Gorodsky, C. Polar actions on compact symmetric spaces which admit a totally
geodesic principal orbit, Geom. Dedicata, 2004.
6. Gorodsky, C., Enlarging totally geodesic submanifolds of symmetric spaces to minimal
submanifolds of one dimension higher, Proc Amer Math. Soc., 2004.
7. Püttmann, T., Rigas, A., Isometric acttions on Projective planes an embeded
generators of homotopy groups, Archiv der Mathematik, 82, 185-192, 2004.
8. Sa Earp, R., Toubiana, E., Meromorphic data for mean curvature one surfaces in
hyperbolic three space, Tohoku Mathematical Journal, 56, 27-64, 2004.
9. Alencar, H., do Carmo, M., Elbert, M. F., Stability of Hypersurfaces with Vanishing rMean Curvatures in Euclidean Spaces, Journal fur Die Reine und Angewandte
Mathematik, 554, 201-216, 2003.
10. Alias, L., Brasil, A., Colares, A. G., Integral formulae for spacelike hypersurfaces in
conformally stationary spacetimes and applications, Proc. Edinb. Math. Soc, 46, 465488, 2003.
11. Barbosa, J. N., Costa, E. A., Lazaro, I. C., Hypersurfaces of the euclidean sphere with
nonnegative Ricci curvature, Arch. Math. (Basel), 81, 335-341, 2003.
12. Brasil, A., Colares, A. G., Palmas, O., Complete spacelike hypersurfaces with constant
mean curvature in the de Sitter space: a gap theorem, Illinois J. Math, 47, 847-866,
2003.
13. Corro, A. V., Ferreira, W., Tenenblat, K., Minimal surfaces obtained by Ribaucour
transformations, Geometriae Dedicata, 96, 117-150, 2003.
14. Corro, A. V., Ferreira, W., Tenenblat, K., Ribaucour transformations for constant mean
curvature and linear Weingarten surfaces, Pac. J. Math, 212, 265-296, 2003.
15. Frensel, K., Fornari, S., Santo, N. E., Ripoll, J. B., Constant mean curvature
hypersurfaces in a Lie group with a bi-invariant metric, Manuscripta Mathematica, 111,
459-470, 2003.
16. Fusieger, P., Ripoll, J. B., Radial graphs of constant mean curvature and doubly
connected minimal surfaces, Annals of Global Analysis and Geometry, 23, 373-400,
2003.
17. Gorodsky, C, G. Thorbergsson, The classification of taut irreducible representations, J
Reine Angew Math., 555, 187-235, 2003.
18. Magli, R. Giambò, F. Giannoni, P. Piccione, New mathematical framework for
spherical gravitational collapse, Classical and Quantum Gravity, 20(6), 75-82, 2003.
19. Magli, R. Giambò, F. Giannoni, P. Piccione, New Solutions for the Einstein's Equations
in Spherical Symmetry: The Cosmic Censor to the Court, Communications in
Mathematical Physics, 235(3), 545-563, 2003.
20. Masiello, P. Piccione, On the Spectral Flow in Lorentzian Manifolds}, Annali di
Matematica Pura e Applicata, 182, 81-101, 2003.
21. Piccione, P., Tausk, D, On the Distribution of Conjugate Points along semiRiemannian Geodesics, Communications in Analysis and Geometry, 11(1), 33-48,
2003.
22. Riveros, C. C., Tenenblat, K., On four dimensional Dupin hypersurfaces in Euclidean
space, Anais da Acad. Bras. Ciências, 75, 1-7, 2003.
61
23. Sa Earp, R., Toubiana, E., Meromorphic data for mean curvature one surfaces in
hyperbolic space, II, Clay Math. Proceedings, 3, 521-540, 2003.
24. Souza, M., Spruck, J., Tenenblat, K., A Bernstein type theorem on a Randers space,
Math. Annalen, 329, 291-305, 2003.
25. Souza, M., Tenenblat, K., Minimal surfaces of rotation in Finsler space with a Randers
metric, Math. Annalen, 325, 625-642, 2003.
26. Tenenblat, K., Minimal and cmc surfaces obtained by Ribaucour transformations, Clay
Mathematics Proceedings, 3, 623-634, 2003.
27. Alencar, H., Carmo, M. P., and Santos, W., A gap theorem for hypersurfaces of the
sphere with constant scalar curvature one, Commentarii Mathematici Helvetici, 77,
549-562, 2002.
28. Arraut, L. and Schweitzer, P.A., A note on actions of the cylinder S1 x R, Topology and
its Applications, 123, 533-535, 2002.
29. Asperti, A. C., and Lobos, G., Mercuri, F., Pseudo-parallel submanifolds of a space
form, Advances in Geometry, 2, 57-71, 2002.
30. Barbosa, J. L., Lira, J. H., Oliker, V., A priori estimates for starshaped compact
hypersurfaces with prescribed m-th curvature function in space forms, Non Linear
Problems in Matematical Physics and related Topics, 1, 35-52, 2002.
31. Barbosa, J.L., Fukuoka, R., and Mercuri, F., Immersions of Finite Geometric Type in
Euclidean Spaces, Annals of Global Analysis and Geometry, 23, 301-315, 2002.
32. Barros, A.A., Applications of Bochner formula to minimal submanifold of the sphere,
Journal of Geometry and Physics, 44,196-201, 2002.
33. Berard, P., Lima, L.L., Rossman, W., Index Growth of Hypersurfaces with Constant
Mean Curvature, Math. Z., 239, 99-115, 2002.
34. Biliotti, L., Mercuri, F., and Tausk, D. V., A Note on Tensors on Hilbert Spaces, Anais
da Academia Brasileira de Ciências, 74, 207-210, 2002.
35. Birbrair, L., Brasselet, J.P., Metric Homology for Isolated Conical Singularities. Bulletin
des Sciences Mathematiques, 126, 201-216, 2002.
36. Carmo, M.P., H-Hypersurfaces with finite total curvature, atas de congresso
Differential Geometry Valencia 2001. An International Meeting on the Occasion of the
60th Birthday of A.M. Naveira, 134-142. (Editors: Olga Gil Medrano e Vicente Miguel),
Wold Scientific, Singapura, 2002.
37. Dajczer, M., Tojeiro, R., An extension of the classical Ribaucour transformation. Proc.
London Math. Society, 85, 211-232, 2002.
38. Ding, Q., Tenenblat, K., Gauge equivalence of differential equations describing
surfaces of constant Gaussian curvature, International Journal of Differential
Equations and Applications, 4, 273-284, 2002.
39. Ding, Q., Tenenblat, K., On Differential systems describing surfaces of constant
curvature, Journal of Differential. Equations, 184, 185-214, 2002.
40. Duran, C., Mendoza, A., Rigas, A., Blakers Massey Elements and exotic
diffeomorphisms of S6 and S14, Trans. Amer. Math. Soc., 93, 11-23, 2002.
62
41. Earp, R.S., Toubiana, E., Discrete and non-Discrete Isometric Deformations of
Surfaces in R 3. Sibirskii Mathematicheskii Zhurnal, 43, 887-893, 2002.
42. Ferreira, M. J., Tribuzy, R., Codimension two Kähler Submanifolds of Space Forms,
Archiv der Matematik, 79, 520-528, 2002.
43. Fornari, S., Lira, J.H., and Ripoll, J., Geodesic Graphs with Constant Mean Curvature
in Spheres, Geometria Dedicata, 90, 201-216, 2002.
44. Gorodsky, C, G. Thorbergsson, Variationally complete actions on compact symmetric
spaces, J. Differential Geom., 62, 39-48, 2002.
45. Hauswirth, L., Roitman, P. and Rosenberg, H., The geometry of finite topology Bryant
surfaces quasi-embedded in a hyperbolic manifold, Journal of Differential Geometry,
60, 55-101, 2002.
46. Hinojosa, P.A., Graphs with Constant Mean Curvature in the 3-Hyperbolic Space,
Anais da Academia Brasileira de Ciências, 74, 371-377, 2002.
47. Hinojosa, P.A., Surfaces of Constant Mean Curvature in Euclidean 3-Space
Orthogonal to a Plane along its Boundary, Anais da Academia Brasileira de Ciências,
74, 33-36, 2002.
48. Lima, L.L., and Roitman, P., Constant Mean Curvature one surfaces in Hyperbolic 3Spaces Using the Bianchi-Calò method, Anais da Academia Brasileira de Ciências,
74, 19-24, 2002.
49. Lira J.H., Embedded Hypersurfaces in Sn+1 with Constant Mean Curvature and
Spherical Boundary, Annals of Global Analysis and Geometry, 21, 123-133, 2002.
50. Lira, J. H., Fornari, S., Ripoll, J. B., Geodesic graphs with constant mean curvature in
spheres, Geometriae Dedicata, 90, 201-216, 2002.
51. Lira, J. H., hypersurfaces in Sn+1 with constant mean curvature and spherical
boundary, Annals of Global Analysis and Geometry, 21, 123-133, 2002.
52. Lira, J. H., Radial graphs with constant mean curvature in the hyperbolic space,
Geometriae Dedicata, 93, 11-23, 2002.
53. Lira, J.H., Radial Graphs with Constant Mean Curvature in the Hyperbolic Space,
Geometria Dedicata, 93, 11-23, 2002.
54. Mercuri, F., Piccione, P., and Tausk, D. V., Stability of the Focal and Geometric Index
in semi-Riemannian Geometry via the Maslov Index, Pacific Journal of Mathematics,
206, 375-400, 2002.
55. Nelli, B., Rosenberg, H., Minimal surfaces in H x R, Bulletin of the Brazilian
Mathematical Society, New series, 33, 263-292, 2002.
56. Piccione, P., Some Global Properties of Static Spacetimes, Mathematische Zeitschrift,
244, 457-468, 2002.
57. Pina, R., Tenenblat, K., On metrics satisfying equation Rij-Kgij/2=Tij for constant
tensors T, Journal of Geometry and Physics, 40, 379-383, 2002.
58. Rosenberg, H., Bryant surfaces, Lectures Notes in Mathematics., Springer-Verlag,
1775, 67-111, 2002.
59. Rosenberg, H., Minimal surfaces in M2 x R, Illinois J. of Math, 46, 1117-1195, 2002.
63
60. Sato, J. Stability of O(p+1)xO(p+1)-invariant Hypersurfaces with Zero Scalar Curvature
in Euclidean Space, Annals of Global Analysis and Geometry, vol 22 (2002), 135-153,
2002.
61. Tenenblat, K., On Ribaucour transformations and applications to linear Weingarten
surfaces, Anais da Academia Brasileira de Ciências, 74, 559-575, 2002.
62. Xia, C. Y., On a conjecture by Schroeder and Strake, Quart. J. Math., 53, 119-124,
2002.
63. Xia, C.Y., Complete manifolds with sectional curvature bounded below and large
volume growth, Bull. London Math Soc., 34, 229-235, 2002.
64. Xia, C.Y., Large volume growth and the topology of open manifolds, Math. Z., 239,
515-526, 2002.
65. Xia, C.Y., Some applications of critical point theory of distance functions on
Riemannian manifolds, Compositio Math, 132, 49-55, 2002.
Articles Accepted for Publication
1. Ripoll, J. B., Fornari, S., Killing fields, mean curvature, translation maps. Illinois journal
of mathematics, 2004.
2. Rosenberg, H., Meeks, W., The uniqueness of the helicoid and the asymptotic
geometry of properly embedded minimal surfaces with finite topology, Annals of Math.,
2004
3. Tenenblat, K., Corro, A. M. V., Ribaucour Transformations Revisited, Communications
in Analysis and Geometry, 2004.
4. Tenenblat, K., Riveros, C. M. C., Dupin Hypersurfaces in R 5, Canadian J. Math., 2004.
5. Abresch, U., Rosenberg, H., A Hopf differential for constant mean curvature surfaces
in SxR and HxR, Acta Math., 2003.
6. Alias, L., Barros, A. A., Brasil, A. A., A Spectral characterization of H(r)-torus by the
first stability Eigenvalue, Proceedings of AMS, 2003.
7. Alias, L., Brasil, A., Sousa Jr., L. A., A characterization of Clifford tori with constant
scalar curvature one by first stability eigenvalue, Buletin of the Brazilian Mathematical
Society, 2003.
8. Alias, L., Lira, J. H., Malacarne, M., Constant higher order curvature hypersurfaces in
Riemannian spaces, Proceedings of the London Mathematical Society, 2003.
9. Almeida, S. C., Brasil, A., Sousa Jr., L. A., Minimal Submanifolds in S3+p with
nonnegative scalar curvature, Results in mathmematics, 2003.
10. Barbosa, J. L. M., do Carmo, M. P., On stability of cones in Rn+1 with zero scalar
curvature, Anais da Acad. Bras. Ciencias, 2003.
11. Brasil, A., Barros, A. A., Sousa Jr., L. A., A New Characterization of submanifolds with
paralell mean curvature vector in Spheres, Kodai Mathematical Journal, 2003.
12. Colin, P., Kusner, R., Rosenberg, H., The topology, geometry and conformal
structures of properly embedded minimal surfaces, J. Diff. Geometry, 2003.
64
13. Dajczer, M., Florit, L., A counterexample to a conjecture on flat bilinear forms, Proc.
Amer. Math. Soc, 2003.
14. Dajczer, M., Florit, L., Genuine rigidity of Euclidean submanifolds in codimension two,
Geom. Dedicata, 2003.
15. Dajczer, M., Tojeiro, R., Commuting Codazzi tensors and the Ribaucour
transformation for submanifolds, Results Math., 2003.
16. Dajczer, M., Tojeiro, R., Isometric immersions in codimension two of warped products
into space forms, Illinois J. Math., 2003.
17. Gorodski, C., Olmos, C., Tojeiro, R., Copolarity of isometric actions, Transations of the
American Math. Society, 2003.
18. Lira, J. H., Hoffman, D., Rosenberg, H., Constant mean curvature surfaces in MxR,
Transations of the American Math. Society, 2003.
19. Mercuri, F., Seixas, J. A. P., Cohomogeneiry one Hypersurfaces and Hypersurfaces of
Revolution, Differential Geometry and its Applications, 2003.
20. Pimentel, F., Pacard, F., Attaching handles to Bryant surfaces, Journal of Jussieu
mathematics institute, 2003.
21. Püttmann, T., Rigas, A., Presentations of certain homotopy groups of Unitary groups,
Comm. Math. Helv, 2003.
22. Püttmann, T., Rigas, A., When is RPn x Spin(n) diffeomorphic to Sn x SO(n) and how,
Okayama Univ. Math J., 2003.
23. Rosenberg, H., Alencar, H., Santos, W., On the Gauss Map of Hypersurfaces with
Constant Scalar Curvature in Spheres, Proceedings of the American Mathematical
Society, 2003.
24. Rosenberg, H., Meeks, W., Maximum principles at infinity and applications to minimal
and constant mean curvature surfaces, J. Diff. Geometry.
25. Rosenberg, H., Meeks, W., The theory of minimal surfaces in MxR, Comment. Math.
Helv.
26. Rosenberg, H., Meeks, W., The theory of stable minimal surfaces in MxR, J. Diff.
Geom.
27. Rosenberg, H., Ros, A., A Properly embedded surfaces with constant mean curvature,
Manuscripta Math.
28. Schweitzer, P. A., Walczak, P., Prescribing mean curvature vectors for foliations,
Illinois Journal of Mathematics, 2003.
29. Tenenblat, K., Pina, R., Conformal metrics and Ricci tensors on the sphere, Proc.
Amer. Math. Soc., 2003.
Books and chapters of books published
1. Alencar, H., Geometria Diferencial das Curvas Planas, edição revista, Editora
Associação Instituto Nacional de Matemática Pura e Aplicada, 125p., 2003.
2. Earp, R.S., Introduction à la Geométrie Hyperbolique et aux Surfaces de Riemann.
Segunda edição, ed. Cassini, Paris.
65
3. Rosenberg, H., Some recent developments in the theory of minimal surfaces in 3manifolds, IMPA (coleção do colóquio de Matemática), vol 1, 48 p., 2003.
4. Alencar, H., and Santos, W., Geometria das Curvas Planas, Coleção da XII Escola de
Geometria, realizada em Goiânia, Ed da UFG, UFG, Goiânia, 120 p., 2002.
5. Barbosa, J.L.M., Geometria Hiperbólica, Coleção da XII Escola de Geometria,
realizada em Goiânia, Ed. da UFG, UFG, Goiania, 189 p., ISBN 85-902605-3-4, CDU
514.13, 2002.
Human Resources
Ph.Ds. degrees
1. Adriano Adrega de Moura. Topicos em Teoria de represenatacoes de Groupos
Quânticos
2. Antonio Caminha Muniz Neto. Sobre hipersuperfícies em espaços de curvatura
seccional constante
3. Ari Aiolfi. O problema de Dirichlet para equação das superfícies mínimas em domínios
não necessariamente convexos
4. Cleon da Silva Barroso. Alguns Resultados em Geometria e em Análise
5. Elias Marion Guio. Estimativas a priori do gradiente, existência e não existência para
uma equação da curvatura média no espaço hiperbólico.
6. Enrique Echaiz Espinoza. Imersões Isométricas k-umbílicas em Formas Espaciais
7. José Carlos Almeida de Lima, Hipersuperficies de revolução nas esferas.
8. José Nelson Bastos Barbosa. Estimativas do Primeiro Autovalor do Laplaciano e
Caracterização de Hipersuperfícies Isoparamétricas em Sn+1
9. Leonardo Biliotti, Alguns aspectos da geometria riemanniana das variedades de
Hilbert.
10. Leonardo Navarro de Carvalho, Automorfismos genéricos de cubos com alças.
11. Luis Fernando Crocco Afonso. Representações de Grupos Triangulares em
Geometria Hiperbólica Complexa
12. Marcos Alexandrino. Folheações Riemannianas Singulares com Seções e Aplicações
Transnormais
M.Sc. degrees
1. Ana Acácia Pereira Valente. Redução de Codimensão de Imersões Regulares em
Espaços Euclidianos
2. Antonio Teófilo Ataíde do Nascimento. Distância Geodésica em conjuntos
subanalíticos
3. Cícero Pedro de Aquino. Uma caracterização de hipersuperfícies na esfera com
curvatura escalar constante.
4. Domingos Anselmo Moura da Silva. Imersões Isométricas de Variedades Kählerianas
66
5. Francisco Etval da Silva Feitosa. Generalização do Teorema de Hopf para uma classe
de superfícies de Weingaren
6. Francisco Valdemiro Braga. A unicidade para superfícies de curvatura média
constante com fronteira
7. Gildo Jesus Sousa, UFC, Julho de 2002. Hipersuperfícies com Duas Curvaturas
Intermediárias Consecutivas Constantes.
8. Henrique Fernandes de Lima, (UFC) Janeiro 2002. Formulas Integrais Tipo-Minkowski
para Hipersuperfícies Tipo-Espaço em Variedades de Lorentz Conformemente
Estacionárias e Aplicacões.
9. Kellcio Oliveira Araújo, (UnB) Fevereiro de 2002. O Princípio da Tangência para
Hipersuperfícies Relacionadas por uma Curvatura Intermediária.
10. Lucas Conque Seco Ferreira, (UnB) Dezembro de 2002. Tinitas ou Infinitas
Geodésicas Riemannianas entre Dois Pontos? Uma aplicação de métodos
Variacionais
11. Luis Fernando Coelho Amaral. Equação de Liouville e superfícies mínimas sem
pontos umbílicos
12. Lyngnys Emmanuel de Arruda Vasconcelos Saraiva. Estimativas Inferiores dos
autovalores do Laplaciano
13. Márcia Sekeff Budaruiche Lima. Superfícies de revolução com curvatura média
periódica
14. Márcio Mazz. Compacidade fraca em espaços de Banach e aplicações de um
teorema de R.C. James
15. Marcio Nascimento Silva. O Problema de Steklov
16. Maria Silvana Alcântara Costa. Decomposição espectral do Laplaciano numa
variedade Riemanniana
17. Pedro Antonio Soares Júnior, UFC, Março de 2002. Sobre Imersões Mínimas de S2
em S4
18. Raul Rabelo Mesquisa. Variedade de Hadamard e Axioma da Visibilidade
19. Ricardo Verotti Oliveira Teixeira. Análise não linear em espaços hiperbólicos
20. Roberto Antonio Cordeiro Prata, UA. Imersões de Variedades com Curvaturas
Seccionais não negativas
21. Rogério César dos Santos. H-deformações de superfícies no espaço euclidiano
22. Sérgio de Moura Almaraz. Geometrias de Thurston e Fibrados de Seifert
23. Sissi da Silva Souza, UA. Hipersuperfícies de Formas Espaciais Reais
24. Waltemir Martins Cabral, UA. Extensão do Teorema de Rauch para Subvariedades
Contributions of IM-AGIMB to the developments of Differential Geometry in Brazil
With the fruitful help of IM-AGIMB mobility has sharply increased allowing a more
consistent interaction between researchers. In addition, the IM it was fundamental in the
success of the several geometry meetings being held in the country. In particular,
67
researches working in more remote parts of the country has a frequent chance to meet
and interact with his fellow researchers from developed regions.
The following meetings took place during the period
1. Workshop on the Geometry of Sub-manifolds and Chaotic Dynamics, UFAL, January
20-30, 2004.
2. Post-Doctoral Summer Activities, UFCe, 2002-2003 and 2005 to be held.
3. Workshop on Surfaces of Constant Mean Curvature and Partial Differential Equations,
Canela - RS, April 26-30, 2004.
4. XIII School of Different Geometry, USP-SP, July 26-30, 2004.
68
The research group in commutative algebra and algebraic geometry under the Millennium
Institute consists of 12 members, networked with a universe of collaborators at least triple
this figure in nearly 10 universities across the country. The number of pre-doctoral and
doctoral students amount to 20 circa at the moment of this report. The group keeps a
foreign collaboration portfolio that includes more than 30 renowned institutions spread
across 11 countries. It goes without saying that all members are presently productive and
research-oriented, a status that provides the group with scientific leadership at national
level while spurring its growing international insertion. The publication, which is highly
diversified, has appeared in reputed mathematical journals such as Amer. Math. J.,
Inventiones, Math. Ann., J. Algebraic Geometry, Compositio Math., to mention a few.
Below we briefly describe the contents of the publication in the period followed by the
complete list of articles published or accepted for publication.
Birationality criteria among projective varieties: In this context we established an
algebraic criterion (i.e., in terms of special rings and modules) for birationality. The final
expression of the criterion is given in terms of a certain polynomial matrix and of its
content. As a bonus we obtained, in an explicit way, the inverse of a birational map.
Furthermore, several conjectures were made and, if proved, they would imply curious new
consequences of the theory.
Algebraic theory of free divisors: We focused, in the polynomial context, on Saito’s free
divisors. With this approach we obtained various results, without assuming the analytic
antecedents. We found alternative notions for the free Koszul divisor, introduced by the
school of Sevilha, retrieving some of their results in the polynomial case. In parallel, we
produced a counter-example for the non-existence of homogeneous irreducible free
divisors in three variables.
Rees algebras of special modules: This is a wide subject of variable contour. The work
already done reflects the cumulative effort of developing a general theory of Rees algebras
(“blowup”), in the case of modules and represents an ample repertoire of the theory of
modules and ideals with emphasis on the homological and generic properties. As a
consequence, some partial results were obtained, in collaboration with B. Ulrich (Purdue
U.) and W. Vasconcelos (Rutgers U.), on the Rees algebra of the module of Kähler
differentials of an affine algebra.
The arithmetic of elliptic curves: Given a fibration of algebraic varieties defined over a
number field, we generalized, in collaboration with M. Hindry (Paris VII), a previous result
for the case of fibrations in curves of a surface over a curve. We proved that the sum of
the rank of the Mordell-Weil group of the Picard variety of the generic fibre with the rank of
the Néron-Severi group of this fibre may be obtained as the sum of residues of Dirichlet
series, whose coefficients are mean traces of the étale Frobenius automorphism, relative
to the first and second cohomology groups, if, and if, the Tate conjecture, for divisors, is
true for both varieties. As an application of this result to the non-trivial problem of studying
69
the variation of the rank of abelian varieties over function fields, we obtained an estimate
of what happens with the rank of an abelian variety over the field of functions of a curve
over a number field, when one extends the base by a Galois covering defined over the
given field of numbers. In particular, when one considers towers of function fields over
number fields that arise from torsion points of elliptic curves and Jacobian varieties, the
mean rank of the abelian variety along the tower is less than the predicted one by the
heuristic.
D-modules: The main advances were obtained in two directions, namely: the creation of
algebraic algorithms to determine if a given foliation of the complex projective plane has an
algebraic solution (in collaboration with L. M. Schechter, an undergraduate student) and
the determination of new families of simple derivations and their applications. In the first
case, we obtained a fast algorithm that establishes another link between the theory of
foliations and algebra, through the use of the Galois group. In the second case, we got a
characterization of a large family of simple derivations in the polynomial ring, in addition to
the construction of new examples of non-holonomic simple D-modules over affine varieties
with non-trivial Picard group.
Arithmetic characterization of fields, via valorization theory (Krull) and the theory of
quadratic forms (Witt): We continued to study the profinite groups, in particular of pro 2grups with cohomological dimension less or equal than two. This research it has been
developed in collaboration with D. Kochloukova (Unicamp) and P. Zalesskii (UnB). In the
work on the structure of Galois groups of the maximum p-extension of fields, we
succeeded to describe these Galois groups as groups that can be obtained from certain
"basic" groups through the operations of free product and semidirect product in the
category of pro p-groups. Extending “Kaplansky’s radical” concept for odd primes it was
possible to determine the arithmetical nature of the free component, whose existence is
established by the Subgrupo Theorem of Kurosh, associating it to the radical of the field.
As a consequence of our work on pro 2-groups with cohomological dimension 2, and the
study of the radical of a field, it was established the validity of the known Conjecture of
Elementary Type for fields with trivial radical. These results are being extended to fields
with non-trivial radical. This is particularly interesting since the triviality of the radical is not
maintained under finite extensions.
Algebraic and holomorphic foliations: In collaboration with S. Kleiman (MIT), we
described the properties of algebraic sets invariant by foliations, obtaining several results
that generalize and improve results of Jouanolou, Lins Neto, Soares, Campillo, Carnicer,
Du Plessis and Wall, related to the Poincaré problem. It was proved that the only proper
invariant subvariety of a generic foliation over a non-singular projective variety consists of
isolated points. We also constructed examples of foliations without algebraic solutions.
Enumerative geometry: We accomplished a substantial advance in the understanding of
the family of curves of genus 2 embedded in degree 5 in P3. For the corresponding case in
the plane, namely, the family of pentagons, also defined by a quadric and two cubics, we
determined explicitly a sequence of blowups (they are 7) to find a good space of
parameters. We also obtained an explicit description of a sequence of blowups that
flattens the family whose general member is the union of a conic and two points in P3. This
appears naturally as one of the centers of blowing-ups in the original case of interest:
degeneration of complete intersections. Several computational routines were developed to
perform the relevant computations to the problem.
70
Rational points of curves over finite fields: We realized explicit constructions of curves
with many points over finite fields, obtaining in particular new records for certain genera
and finite small fields. We obtained general results on the classification of certain maximal
curves from their genus and with hypotheses on their Weierstrass gaps in a rational point,
generating a source of examples of maximal curves of same genus and not isomorphic to
each other. We obtained necessary restrictive conditions for Artin-Schreier type towers
with good asymptotic behavior for the ratios of the number of rational points and genus,
advancing in the direction of their classification. We also constructed a new tower (simpler
than the existing ones) of fields of functions over finite fields, with square cardinality,
attaining the Drinfeld-Vladut bound. We point out as an important contribution the
construction of tower of function fields over finite fields of cubic cardinality with a record
limit of the above ratios, generalizing a bound obtained by T. Zink. Some of this work was
done in collaboration with H. Stichtenoth (Essen U.).
Linear systems over families of curves and their limits: We realized a study of limits of
ramification points of linear systems on families of plane curves. This problem is a
generalization of the one studied by Zeuthen in the nineteenth century in his computation
of characteristic numbers of cubics and quartics. We described the degeneration of linear
systems for an irreducible singular curve, completing the work of Lax and Widland done in
the 80’s. We also described degeneration of Weierstrass points for a nodal irreducible
curve, extending results we obtained earlier, answering a question raised by Eisenbud and
Harris also in the 80’s.
Fibre bundles over curves: We studied, in collaboration with S. Kleiman (MIT), the
compactified Jacobian, that parametrizes degeneration of line bundles over an irreducible
curve. If the curve is not too much singular, it was proved that such an object is autodual,
that is, there exists a natural isomorphism among its Picard scheme and the Jacobian of
the curve. Recently, it was shown that this isomorphism extends to compactifications.
Nevertheless recent, these results were applied in works by G. Laumon and J. Sawon. We
also developed, in collaboration with M. Popa, a work on generalized theta divisor on the
moduli of vector bundles with constant determinant over a smooth curve. We found an
effective bound for when divisors, linearly equivalent to a multiple of the theta divisor,
embed the moduli space.
Algebraic theory of singularities: We achieved significant progress in the classification,
under the action of the contact group, of the germs of analytic curves in a given
equisingularity class. We found normal forms and did the complete classification of such
germs in several particular equisingularity classes and, notably, of all germs of multiplicity
2, 3 and 4. We developed theoretic-computational methods to determine relevant
numerical invariants to perform the classification. We also succeeded to describe the
invariant part of the roots of the Bernstein-Sato polynomials associated to topologically
trivial families of isolated singularities of complex hypersurfaces.
The role of this institution was key in the support of the following fundamental strategies for
progress in the area:
•
•
•
•
Specialized meetings
Interchange with foreign institutions
Cooperation between established centers and emerging research groups
Extending the cooperation research with Latin American counterparts and students
71
Papers published or accepted for publication
1. A. Engler, A recursive description of pro-p-Galois groups, Journal of Algebra, 274,
511-522, 2004.
2. A. Engler, D. Haran, D. Kochloukova and P. Zaleskii, Normal subgroups of profinite
groups of finite cohomological dimension, J. London Math. Society, 69, 317-332, 2004.
3. A. Garcia and J. Bezerra, A Tower with non–Galois steps which attains the Drinfeld,
Vladut Bound, J. Number Theory, 106, 42-154, 2004.
4. A. Garcia and M. Abdon, On a Characterization of certain maximal curves, Finite
Fields Appl., 10, 133-158, 2004.
5. A. Garcia, H. Stichtenoth and P. Beelen, On ramification and genus of recursive
towers, Portugaliae Math., 2004.
6. A. Garcia, P. Beelen and H. Stichtenoth, On Towers of function fields of Artin–
Schreier Type, Bull. Brazilian Math. Soc., 35, 151-164, 2004.
7. A. Pacheco and M. Hindry, Sur le rang des Jacobiennes sur un corps de fonctions,
Bull. Soc. Math. de France, 2004.
8. A. Pacheco, M. Hindry and R. Wazir, Conjectures de Tate et fibrations, J. of Number
Theory, 2004.
9. A. Simis, Cremona Transformation and some related algebras, J. Algebra, 2004.
10. A. Simis, Differential idealizers and algebraic free divisors, in Lect. Notes in P. and
Appl. Math., Marcel Dekker, 2004.
11. E. Esteves and M. Popa, Effective very ampleness for generalized theta divisors, Duke
Math Journal, 122(3), 429-444, 2004.
12. E. Esteves and S. Kleiman, Bounds on leaves of foliations of the plane, Contemporary
Math., 2004.
13. F. Russo and A. Alzati, Some elementary extremal contractions between smooth
varieties arising from projective geometry, Proc. London Math. Soc., 89, 25-53, 2004.
14. F. Russo and C. Ciliberto, On surfaces with two apparent double points, Adv. in
Geometry, 2004.
15. F. Russo, C. Ciliberto and M. Mella, Varieties with one apparent double point, J. Alg.
Geom., 13, 475-512, 2004.
16. F. Torres and C. Carvalho, On Goppa codes and Weierstrass gaps at several points.
Des. Codes Crypt., 2004.
17. F. Torres and C. Munuera, Bounding the trellis state complexity of algebraic geometric
codes, Appl. Alg. Eng. Comm. Comput., 2004.
18. F. Torres and M. Giulietti, On dense sets related to plane algebraic curves. Ars
Combinatoria, 2004.
19. I. Vainsencher and J. Koch, Kontsevich’s formula for rational plane curves, Birkhäuser,
2004.
20. I. Vainsencher and F. Xavier, Numbers for reducible cubic scrolls, Anais da Academia
Brasileira de Ciências, 2004.
72
21. I. Vainsencher, Sur le nombre de singularités dégénérées d’une famille de
feuilletages, Math. Research Letters, 11(4), 2004.
22. S. Collier, Primalidade em tempo polinomial, published by SBM, Brazilian
Mathematical Society, 2004.
23. S. Collier, Quotient rings of noncommutative rings in the half of the 20th century, Arch.
Hist. Exact Sci., 58(3), 255-281, 2004.
24. A. Garcia and A. Garzon, On Kummer covers with many rational points over finite
fields, J. Pure Appl. Algebra, 185, 177-192, 2003.
25. A. Garcia and H. Stichtenoth, On tame towers over finite fields, J. Reine Angew Math.
557, 53-80, 2003.
26. A. Hefez, Irreducible Plane Curve Singularities, in Lecture Notes in Pure and Applied
Math., 232, Marcel Dekker, 1-120, 2003.
27. A. Hefez and M. E. Hernandes, Classification of algebroid curves with semigroup <6,
9, 19>, Comm. in Algebra, 31, 3847-3861, 2003.
28. A. Pacheco, Distributions of the traces of Frobenius on elliptic curves over function
fields, Acta Arithmetica, 106(3), 255-263, 2003.
29. A. Simis, Two differential themes in characteristic zero, Contemporary Math., 324,
195-204, 2003.
30. A. Simis and R. Villarreal, Constraints for the normality of monomial subrings and
birationality, Proc. Amer. Math. Soc., 131, 2043-2048, 2003.
31. A. Simis, B. Ulrich and W. Vasconcelos, Rees algebras of modules, Proc. London
Math. Soc., 87(3), 610-646, 2003.
32. E. Esteves and L. Gatto, A geometric interpretation and a new proof of a relation of
Cornalba and Harris, Comm. in Algebra, 31, 3753-3770, 2003.
33. E. Esteves and S. Kleiman, Bounding solutions of Pfaff equations, Communications in
Algebra, 31, 3771-3793, 2003.
34. E. Esteves and S. Kleiman, Bounds on leaves of one–dimensional foliations, Bulletin
Braz Math Soc. 34, 145-169, 2003.
35. F. Russo, Tangents and Secants of Algebraic Varieties, Publicações Matemáticas,
IMPA, 2003.
36. F. Russo and A. Alzati, Special subhomaloidal systems of quadrics and varieties with
one apparent double point, Math. Proc. Camb. Phil. Soc., 134 (1), 65-82, 2003.
37. F. Torres and C. Carvalho, On numerical semigroups related to coverings of curves.
Semigroup Forum 67, 344-354, 2003.
38. F. Torres and C. Munuera, A Goppa-like bound on the trellis state complexity of
algebraic geometric codes, IEEE Trans. Inform. Theory, 49 (3), 733–737, 2003.
39. S. Collier, Indecomposable non–holonomic D–modules in dimension 2, Proc.
Edinburgh Math. Soc., 46, 341-355, 2003.
40. S. Collier, Non-holonomic irreducible D-Modules over complete intersections, Proc.
Amer. Math. Soc., 131, 83-86, 2003.
73
41. S. Collier, On the differential simplicity of polynomial rings, J. of Algebra, 264, 442-468,
2003.
42. S. Collier and J.C. Mc Connell, The quest for quotient rings, Amer. Math. Monthly, 110,
298-313, 2003.
43. Y.Lequain, P. Brumatti and D. Levcovitz, Differential simplicity in polynomial rings and
algebraic independence of power series, J. London Math. Soc., 68, 615-630, 2003.
44. A. Garcia and Y. Lequain, Elementos de Álgebra, Projeto Euclides, IMPA, 2002.
45. A. Hefez and M. L. T. Villela, Códigos Corretores de Erros, Série de Computação e
Matemática, IMPA, 2002.
46. A. Simis, K. Smith and B. Ulrich, An algebraic proof of Zak’s inequality for the
dimension of the Gauss image, Math. Z., 241, 871-881, 2002.
47. A. Simis, P. Brumatti, Y.Lequain and D. Levcovitz, A note on the Nakai conjecture,
Proc. Amer. Math. Soc., 130, 15-21, 2002.
48. E. Esteves, The Castelnuovo-Mumford regularity of an integral variety of a vector field
on projective space, Math. Res. Letters, 9(1), 1-15, 2002.
49. E. Esteves and N. Medeiros, Limit canonical systems on curves with two components.
Invent. Math., 149(2), 267-338, 2002.
50. E. Esteves, M. Cagne and S. Kleiman, Autoduality of the compactified Jacobian, J.
London Math. Soc., 56(3), 591-610, 2002.
51. F. Russo, The antibirational involutions of the plane and the classification of real del
Pezzo surfaces, in Algebraic Geometry de Gruyter volume in memory of Paolo
Francia., 289-312, 2002.
52. F. Russo and A. Alzati, On the k-normality of projected algebraic varieties, Bull Braz.
Math. Soc., 33(1), 27-48, 2002.
53. F. Russo and A. Alzati, The usual Castelnuovo's lemma and subhomaloidal linear
system of quadrics, Le Matematiche, LV (II), 373-385, 2002.
54. F. Torres and G. Korchmaros, On the genus of a maximal curve, Math. Ann., 323 (3),
589-608, 2002.
55. F. Torres, M. Giulietti, F. Pambianco and E. Ughia, On complete arcs arising from
plane curves, Des. Codes Cryptogr. Estados Unidos, 25 (3), 237-246, 2002.
56. F. Torres, M. Giulietti, F. Pambianco and E. Ughia, On large complete arcs: odd case,
Discrete Mathematics, 255, 145-159, 2002.
57. I. Vainsencher, Hypersurfaces with up to six douple points, Communications in
Algebra, 31 (9), 4107-4129, 2002.
58. I. Vainsencher and F. Xavier, A compactification of the space of twisted cubics, Math.
Scand., 91 (2), 221-243, 2002.
59. I. Vainsencher and J. Rojas, Canonical curves in P3, Proc. London Math. Soc., 85 (3),
333-366, 2002.
60. N. Medeiros, On canonical curves and osculating spaces, J. Pure Appl. Alg., 170, 267285, 2002.
74
Ph.Ds. Theses
1. Juscelino Bezerra dos Santos, Duas Torres de Corpos de Funções sobre corpos
finitos e as cotas de Drinfeld– Vladut e de Zink, 2004. Advisor: Arnaldo Garcia, IMPA.
2. Ercilio Carvalho da Silva, TBA, 2003. Advisor: Fernando Torres Orihuela, Unicamp.
3. Parham Salehyan, Pontos de Weierstrass limites em curvas nodais, 2003. Advisor:
Eduardo Esteves, IMPA.
4. Patrícia Helena Araújo da Silva Nogueira, Limites de sistemas lineares em Curvas de
Gorenstein, 2003. Advisor: Eduardo Esteves, IMPA.
75
Dynamical Systems
The theory of hyperbolic dynamical systems started approximately four decades ago,
aiming at characterize the structurally stable systems and to show they are open and
dense. The first aim was reached, for class C1 systems, by R. Mañé in the 80’s, when he
proved the Palis-Smale conjecture for diffeomorphisms and, for flows, by Hayashi some
ten years later.
Still in the 60’s, it was shown that the class of hyperbolic systems does not exhibit the
universal character which was conjectured at the beginning of that decade. In fact many
important systems, including the majority of those arising from modeling of practical
situations, do not pertain to the hyperbolic systems realm. Such systems present, usually,
a very complex dynamic behaviour whose description, both in phase space and in
parameter space, is done not only geometrically, as it happens in the hyperbolic case, but
also in ergodic or probabilistic terms.
The study of certain models, such as Hénon’s and Lorenz’s chaotic attractors, as well as
the development of important techniques, specially in bifurcation theory and in non-uniform
hyperbolicity led, in the 90’s, to an attempt of formulating a global approach of the
Dynamics aiming at a description of dynamical behaviour which would be as rich as
possible, as well as as generic as possible. Palis contributed to this approach by
formulating the following conjectures:
Every dynamical system can be approximated by a system with only a finite number of
attractors whose basins of attraction contains almost every point.
For systems with a finite number of attractors there are physical probability measures
describing the statistical behaviour of almost every point in the attracting basin. Also, this
behaviour is stable under small random perturbations (stochastic stability).
Moreover, for almost all perturbations of such a system along parametrized families, there
is a finite number of attractors which support physical measures and whose basins of
attraction cover a fraction close to 1 of the initial basins.
In the last few years some definitive progress has been made with respect to these and
other fundamental problems by members of this Project. In the whole, the advances
obtained placed the theory of chaotic dynamical systems in a new level of depth and
extent. They also broadened the perspectives for the development of this program, as
described below.
Homoclinic bifurcations
The works of Newhouse, Palis, Takens, Yoccoz and Moreira developed a powerful
geometric approach to the study of homoclinic tangencies in surfaces. In the higher
dimensional situation a whole new range of difficulties arise specially due to the fact that,
in general, the associated invariant foliations may not de differentiable. For this reason
many basic questions concerning hyperbolic sets remain open or unsolved (e.g., the
definition of Place fractal dimension), or are false (e.g., the continuity of the fractal
dimension) in dimensions greater than 2. Despite these difficulties, Moreira, Palis and
Viana are achieving success in extending, to arbitrary dimensions, the connection between
fractal dimension and the frequency of hyperbolicity in the unfolding of tangencies (C R
Acad. Sci. Paris, 2001).
76
In a remarkable recent work (to appear in Ann. of Math.), Moreira and Yoccoz solved the
Palis conjecture on the arithmetic difference of regular Cantor sets: generically, the
difference has zero measure or non-empty interior. In Yearther article they apply this result
in the context of homoclinic bifurcations and give a surprising “complete” answer to the
problem of hyperbolicity frequency in the unfolding of a tangency.
Following previous work by Palis and Takens, now Palis and Yoccoz are showing in
several cases that the prevalent dynamics, in terms of relative measure in parameter
space, is non-uniformly hyperbolic. The result includes the prevalence of the nonexistence of attractors. Their approach (C R Acad. Sci.Paris, 2001) deepens the relation
between homoclinic tangencies and Hénon type maps and also suggests that non-uniform
hyperbolicity may be prevalent in all the generic cases.
The study of differences of regular Cantor sets has important applications in number
theory (Lagrange and Markov spectra) and, in fact, it happened that some notions (such
as thickness) where independently discovered in the realm of Dynamical Systems and
Number Theory. Exploring connections in these two domains, Moreira showed that the
Hausdorff dimension of the intersection of Lagrange’s spectrum with a half-line may
assume any real value between 0 and 1. An analogous result holds for Markov’s spectrum
and, in fact, the dimensions coincide.
A major recent result is due to Pujals and Sambarino (appeared in Ann. of Maths.). They
proved a Palis’ conjecture stating that any surface diffeomorphism may be C1
approximated by one which is either hyperbolic or admits a homoclinic tangency.
This result had several follow ups, some of which still are in progress. One of them, also
due to Pujals and Sambarino, is the proof that the topological entropy variation along a
family of diffeomorphisms necessarily involves the unfolding of homoclinic tangencies.
Another important development was the detailed description, due to Pujals and
Sambarino, of the invariant sets exhibiting a dominated decomposition (On the dynamics
of dominated splitting, submitted).
In dimensions greater than 2, Palis conjectures that any Cr diffeomorphism may be
approximated by one which is hyperbolic or has a homoclinic tangency or a heteroclinic
cycle. This problem is still a challenge, although Pujals had obtained some encouraging
progress, most recently in dimension 3.
It is also worth conjecturing that, away from homoclinic tangencies, hyperbolicity or a weak
form of hyperbolicity must prevail, as suggested by works of Pujals and Sambarino, among
others. In such cases the global conjecture about finiteness of attractors, stated above,
must be true, a fact already known in the hyperbolic case. Hence, a more deep knowledge
of homoclinic bifurcations may lead to the conclusion of the ambitious program of a global
scenario for the dynamical systems, as stated above.
Partial hyperbolicity and robust transitivity
By a classical work of Mañé, robust attractors of surface diffeomorphisms are hyperbolic.
In higher dimensions this is not true in general. However, Díaz, Pujals and Ures (Acta
Math.) showed that robust attractors in dimension 3 must be partially hyperbolic. Bonatti,
Díaz and Pujals (Ann. of Maths.) extended this result to arbitrary dimension and to
conservative diffeomorphisms: robust attractors always have a dominated decomposition.
A particular relevant case in all these results is when the attractor is the whole manifold.
Besides, Morales, Pacifico and Pujals (Ann. of Maths.) obtained a corresponding
characterization for robust transitive sets of flows, with a singularity.
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In “Maximal transitive sets with singularities for generic vector fields” (Bol. Soc. Bras. Mat.)
and “Homoclinic classes for generic C1 vector fields”, Morales, Pacifico and Carballo
defined maximal transitive set of a diffeomorphism or of a flow and showed that,
generically, homoclinic classes are transitive maximal sets, a fact that answered a
question of Bonatti and Díaz (Ann. ENS 1998). In the last quoted article, Morales, Pacifico
and Carballo characterize the maximal transitive set containing a singularity of a generic
vector field in dimension 3 and also present results relating this work with Bonatti,
Pumariño and Viana (CRAS 1998).
An important consequence of these results is that, for generic systems, the homoclinic
classes are pairwise disjoint. Abdenur uses this to state and prove a spectral
decomposition result - the existence of a finite number of basic elements, which are
persistent and Placely finite in number - for generic systems with a finite number of disjoint
homoclinic classes.
Such systems were called “tame” by Bonatti and Díaz, in contrast to “wild” systems, those
admitting an infinite number of transitive maximal sets. The first examples of wild dynamics
are due to Newhouse: generic coexistence, in the C2 topology, of an infinite number of
sources and sinks. Bonatti and Díaz (Ann. ENS 1998) showed that this pheNamenon is
generic, in the C1 topology, in dimensions greater than 2. In the recent work “On maximal
transitive sets of diffeomorphisms” they present a very general construction of wild
dynamics. While the results by Abdenur exhibit a satisfactory description of tame systems,
based on the fundamental results on robust transitivity and partial hyperbolicity due to
Morales, Pacifico, Díaz, Pujals, Ures and Bonatti, the understanding wild dynamics and its
relation with homoclinic pheNamena is a very interesting research theme in the area.
Holomorphic foliations
The recent research results in holomorphic foliations are progressively making use of
methods of Algebraic Geometry and Analytic Geometry.
M. Soares continued the geometric study of holomorphic foliations, exploring polarity with
respect to foliations. Polar classes are a very interesting concept in Algebraic Geometry
and the aim is the study of polar classes associated to holomorphic foliations.
In the case of surface foliations, the work “Some examples for Poincaré and Painlevé
problems”, by Lins Neto, exhibit families of foliations of constant degree which admit
invariant curves of arbitrarily high degree, showing that the so called Poincaré problem has
a negative answer in general. Its worth remarking that this pheNamenon occurs due to the
presence of dicritical singularities.
In the work “Dicritical singularities of Halphen pencils”, by Sad and Mendes, dicritical
singularities come into play again: under certain conditions involving their multiplicities and
the degree of the foliation, it is shown that the existence of Place first integrals gives rise to
a global first integral.
First integrals were also considered by Camacho and Scardua in “Holomorphic foliations
with Liouvillian first integrals”, where they are obtained through the holonomy group of an
invariant subvariety.
Other works are of geometric character. Lins Neto, in “Uniformization and the Poincaré
metric on the leaves of a foliation by curves” shows that the Poincaré metric on the leaves
of a holomorphic foliation varies continuously under fairly general conditions.
78
Soares, in “On Poincaré’s problem for one-dimensional projective foliations”, associates
characteristic numbers to a foliation and relates them to the polar classes of an invariant
subvariety. Soares also obtained an improvement of Chern’s proof of Baum-Bott’s theorem
(which relates indices of singularities of vector fields to global invariants of the manifold).
In all the above the existence of invariant subvarieties was assumed. But in general
foliations do not admit invariant varieties. The work by Camacho and Figueiredo displays
examples of such a situation.
The work by Cerveau, Edixhoven and Lins Neto, “Pull-back components of the space of
holomorphic foliations on CP (n)” shows that the space of codimension 1 holomorphic
projective foliations has irreducible components made of pull-backs of planar foliations by
rational maps.
By using techniques à lá Grauert, Camacho, Movasati and Sad in “Fibered neighborhoods
of curves in surfaces”, compared linearized neigborhoods of the zero section of the normal
bundle of a curve to a fibered neighborhood of the curve in the manifold. This work has
interesting consequences in the study of the desingularization of foliations with dicritical
singularities.
In “Espaces analytiques coherents et applications”(C R Acad; Sci. Paris, 2004) by Soares,
D. Lehmann e V. Cavalier new characteristic classes for singular varieties are obtained
through methods of K-theory. The obtention of new characteristic classes for singular
varieties is an interesting theme of research.
Conservative systems and ergodic theory
The work of Lopes on conservative systems centers in research on lagrangean flows,
especially Aubry-Mather’s theory and thermodynamical formalism, especially in the
correlation decay of systems defined by non Hölder potentials.
In a recent work Lopes and Exel present a dictionary relating thermodynamical formalism
and ergodic theory of hyperbolic systems to C-star algebras.
In the realm of conservative dynamics there is a work by Dias Carnero and Ruggiero (to
appear in Erg. Theo. And Dyn. Sys.) dealing with variational and topological properties of
invariant tori.
Geometric and statistical properties of attractors
One of the main results obtained is a fairly complete study of the theory of chaotic
attractors of Hénon type, initiated during the end of the 80’s by Benedicks and Carleson.
More precisely, Benedicks and Viana solved the problem of the attracting basin, by
showing that the topological and ergodic attracting basins coincide, up to a set of
Lebesgue probability zero. This means that for almost all points whose orbit converge to
the attractor is statistically described by the physical measure supported on the attractor.
This work was published in Inv. Math. Besides, Benedicks and Viana also show, in a
submitted article, that the dynamics of Hénon type attractors is stochastically stable,
although very unstable from the topologival point of view. This is the first stability result in
dimensions higher than 1 and should establish a paradigm for very general chaotic
systems.
Lyapunov exponents and non-uniform hyperbolicity
This research theme was motivated by several results related to partially hyperbolic
systems, which showed the importance of knowing the behaviour of Lyapunov exponents.
79
Assuming they do not vanish, the general theory of non-uniform hyperbolicity (Pesin’s
theory) gives important geometric information about the dynamical system, such as
showing that the Place stable and unstable manifolds are differentiable discs almost
everywhere. Alves, Bonatti and Viana (Inventiones 2000) showed that, if the exponents of
a partially hyperbolic conservative diffeomorphism are away from zero, then the Lebesgue
measure has only a finite number of ergodic components which are the physical measures
of the system.
In a recent work, Bochi and Viana show that the Lyapunov exponents of Issue preserving
C1 diffeomorphisms vary continuously in a given diffeomorphism f only if either Oseledets’
decomposition is dominated (uniform projective hyperbolicity) or all Lyapunov exponents
are zero almost everywhere. As a consequence, they obtain a strong dichotomy for a
residual set of conservative diffeomorphisms in a manifold: uniform projective hyperbolicity
or total absence of hyperbolicity.
On the other hand, Viana, Bonatti and Gomez-Mont showed that for certain Cr cocycles,
r>0, on hyperbolic systems, the generic behaviour is precisely the opposite of the
continuous case: in most cases (open, dense and with total probability) there are non-zero
exponents.
Unidimensional dynamics
An important result was established by Avila and Moreira in “Statistical properties of
unimodal maps: the quadratic family” (to appear in Ann. of Maths.). Generalizing a result
by Lyubich, they show that, for parametrized families of analytic unimodal transformations
of the interval, there is a unique attractor admitting an absolutely invariant measure with
respect to Lebesgue measure and whose basin attracts every point of the interval with
total probability.
This result is based in Yearther work, by Avila, Lyubich and de Melo, “Regular or
stochastic dynamics in real analytic families of unimodal maps”, which will appear in
Inventiones. It is shown here that the topological conjugation classes make up a quasisymmetric lamination, away from the saddle-node bifurcations, in the space of unimodal
analytic transformations.
Also, Avila and Moreira extended their own result above for the case of class C3 unimodal
transformations in “Statistical properties of unimodal maps: smooth families with negative
Schwarzian derivative” (to appear in Astérisque). Based on a previous work by Baladi and
Viana, they show the stochastic stability of a dense set of such transformations.
Hence the Palis’ conjectures on a global scenario for the dynamical systems, cited at the
beginning of this report, hold true for unimodal transformations of the interval.
Scientific Production - 2004
1. A. Arbieto and C. Matheus, Decidability of chaos for some families of dynamical
systems, Foundations of Computational Mathematics, 4, 269-275, 2004.
2. A. Arbieto, C. Matheus and M.J. Pacifico, Bernoulli property for some partially
hyperbolic conservative systems, Journal of Statistical Physics, ll7, 243-260, 2004.
3. A. Lins Neto and J. Canille Martins, Hermitian metrics inducing the Poincaré metric, in
the leaves of a singular holomorphic foliation by curves, Trans. Amer. Math. Soc.,
2963-2988, 2004.
80
4. A. Lins Neto, D. Cerveau, O.C. Andrade and L. Giraldo, Irreducible components of the
space of foliations associated to the affine Lie algebra, Ergodic Theory and Dynamical
Systems, 2004.
5. A. Lins Neto, On Halphen’s theorem and some generalizations, Annales de l’Institut
Fourier, 2004.
6. C. Camacho, Residues of holomorphic foliations relative to a general submanifold,
Bulletin of the London Mathematical Society, 2004.
7. C. Gutierrez and Benito Pires, On Peixoto’s Conjecture for flows on non-orientable 2manifolds, Proc. of the AMS, 2004.
8. C. Gutierrez and Victor Guíñez, Rank-1 Codimension One Singularities of Positive
Quadratic Differential Forms, Journal of Differential Equations, 2004.
9. C. Gutierrez, A. Fernandes and R. Rabanal, Global asymptotic stability for
differentiable vector fields of ℜ2, Journal of Differential Equations, 2004.
10. C. Gutierrez, A. Fernandes and R. Rabanal, On local diffeomorphisms of ℜn that are
injective, Qualitative Theory of Dynamical Systems, 63, 129-136, 2004.
11. C. Gutierrez, G. Hector and A. López, Interval Exchange Transformations and
foliations on infinite genus twomanifolds, Ergodic Theory and Dynamical Systems, 24,
1097-1108, 2004.
12. C. Gutierrez, R. Garcia and J. Sotomayor, Bifurcations of umbilic points and related
principal cycles, Journal of Dynamics and Differential Equations, 15, 2004.
13. C. Matheus and A.K. Oliveira, Equilibrium states for random non-uniformly expanding
maps, Nonlinearity, 581-593, 2004.
14. C.A. Morales and C. Carballo, Omega-limit sets close to singular-hyperbolic attractors,
Illinois J. Math., 48, 645-663, 2004.
15. C.A. Morales and M.J. Pacífico, Sufficient conditions for robustness of attractors,
Pacific J. Math., 2004.
16. C.A. Morales, 3-manifolds supporting, sov flows and abelian normal subgroups,
Topology and its Applications Volume, 24, 249-255, 2004.
17. C.A. Morales, A note on periodic orbits for singular-hyperbolic flows, Discrete Contin.
Dyn. Syst., 2-3, 615-619, 2004.
18. C.A. Morales, Incompressibility of torus transverse to vector fields, Topology
Proceedings, 2004.
19. C.A. Morales, M.J. Pacifico and E.R. Pujals, Robust transitive singular sets for 3-flows
are partially hyperbolic attractors or repellers, Annals of Mathematics, 160, 1-58, 2004.
20. C.A. Morales, M.J. Pacifico and B. San Martin, Expanding Lorenz attractors through
resonant double homoclinic loops, SIAM J. Math. Anal., 2004.
21. C.A. Morales, M.J. Pacifico and E.R. Pujals, C 1 robust singular transitive sets for threedimensional flows are partially hyperbolic attractors, or repellers Ann. of Math., 2004.
22. C.A. Morales, The explosion of singular-hyperbolic attractors, Ergodic Theory Dynam.
Systems, 2, 577-591, 2004.
23. C.A. Morales, The explosion of singular-hyperbolic attractors, Ergodic Theory Dynam.
Systems, 2, 577-591, 2004.
81
24. C.G. Moreira and Y. Kohayakawa, Bounds for Optimal Coverings, Discrete Applied
Mathematics, 141, 263-276, 2004.
25. C.G. Moreira, A. Avila, Quasisymmetric robustness of the Collet-Eckmann condition in
the quadratic family, Boletim da Soc. Brasileira de Matemática, 2, 2004.
26. E.R. Pujals, M. Sambarino and V. Baladi, Dynamical zeta functions for analytic surface
diffeomorphisms with dominated splitting, J. Inst. Math. de Jussieu, 2004.
27. E.R. Pujals, M.J. Pacífico and J. Vieitez, Generically robustly expansive homoclinic
classes are hyperbolic, Ergodic Theory and Dynamical Systems, 24, 1-30, 2004.
28. E.R. Pujals, M.J. Pacífico and J. Vieitez, Non-wandering sets with non-empty interiors,
Nonlinearity, 1, 175-191, 2004.
29. F. Abdenur, A. Avila and J. Bochi, Robust transitivity and topological mixing for C1
flows, Proc. Amer. Math. Soc, 3, 699-705, 2004.
30. F. Hertz, Stabe ergodicity of some toral automorphisms, Annals of Mathematics, 2004.
31. I. Aguilar, E. Apaza and C.A. Morales, Invariant subsets of volume hyperbolic sets,
Communications in Contemporary Mathematics, 2004.
32. J. Palis, A Global View on non-conservative dynamics. Proc. of the National Academy
of Sciences, 2004.
33. J. Palis, Conjectures and results in non-conservative dynamics, Discrete and
Continuous Dynamics, 2004.
34. J. Vitório and Luis G. Mendes, Hilbert modular foliations on the projective plane,
Commentarii Mathematici Helvetici, 2004.
35. J. Vitório and Paulo Sad, On the holonomy group of algebraic curves invariant by
holomorphic foliations, Annali Della Scuola Normale Superiore Di Pisa, 2004.
36. J. F. Alves, S. Luzzatto and V. Pinheiro, Lyapunov exponents and rates of mixing for
one-dimensional maps, Ergodic Theory Dynam. Systems, 3, 637-657, 2004.
37. J.Medrado and J. Llibre, Darboux integrability and reversible vector fields, Rocky
Mountain Journal, 2004.
38. M. Benedicks and M. Viana, Randon perturbations and statistical properties of Henonlike attractors, Annals de lÍnstitut Henri Poincaré, Analyse Non-Lineaire, 2004.
39. M. Soares, Determination of the top Baum-Bott number via classical intersection
theory, Bull. Braz. Math. Soc., 35, 127-150, 17, 2004.
40. M. Viana and C. Bonatti, Lyapunov exponents with miltiplicity 1 for deterministic
products of matrices, Ergod. Th. & Dynamical Systems, 25, 1-36, 2004.
41. M. Viana, C. Bonatti, C. Matheus and A. Wilkinson, Abundance of stable rgodicity,
Comentarii Math. Helvetici, 79, 2004.
42. M.A.Teixeira and A. Jacquemard, Invariant varieties for discontinuous vector fields,
Nonlineatrity, 2004.
43. M.A.Teixeira and C. Buzzi, Time-reversible Hamiltonian vector fields with symplectic
symmetries, J. of Dynamics and Diff. Eq., 2004.
44. M.A.Teixeira and R.A. Garcia, Vector fields in manifolds with boundary and reversibility
-an expository account, Qualitative Theory of Dynamical Systems, 5(2), 185-200, 2004.
82
45. M.A.Teixeira, C. Buzzi, and P.R. Silva, Singular perturbation problems for timereversible systems, Proceedings of AMS, 2004.
46. M.A.Teixeira, J. Lamb and K. Webster, Heteroclinic bifurcations near Hopf-zero
bifurcation in reversible vector fields in R 3, J. of Diff. Equations, 2004.
47. M.A.Teixeira, S. Mancini and M. Manoel, Divergent diagrams of folds and simultaneous
conjugacy of involutions, Discrete and Continuos Dynamical Systems, 2004.
48. R. Garcia and J. Sotomayor, Lines of Mean Curvature Lines on Surfaces Immersed in
R3, Qualitative Theory of Dynamical Systems, 5(2), 137-183, 2004.
49. V. Cavalier, D. Lehmann and M. Soares, Classes de Chern des ensembles
analytiques, C. R. Math. Acad. Sci. Paris, 11, 879-884, 2004.
50. W. de Melo, Bifurcation of unimodal maps, Qualitative Theory of Dynamical Systems,
5, 285-296, 2004.
51. W. de Melo, E. de Faria and A. Pinto, Global Hyperbolicity of Renormalization for Cr
Unimodal Mappings, Annals of Mathematics, 79, 2004.
1. A. Arbieto, C. Matheus; M.J. Pacifico, The Bernoulli property for weakly hyperbolic
systems, Journal of Statistical Physics, 2003.
2. A. Arbieto, J. Bochi, Lp-generic cocycles have one-point Lyapunov spectrum,
Stochastics and Dynamics, 73-81, 2003.
3. A. Avila, F. Abdenur and J. Bochi, Robust transitivity and topological mixing for C1flows, Proc. of American Mathematical Society, 132, 699-705, 2003.
4. A. Avila, M. Lyubich and W. de Melo, Regular or stochastic dynamics in real analytic
families of nimodal maps, Inventiones Mathematicae, 154, 451-550, 2003.
5. A. Lins Neto and J. Canille Martins, Hermitian metrics inducing the Poincaré metric in
the leaves of a singular foliation by curves, Transactions of the American Math. Soc,
356, 2963-2988, 2003.
6. A. Lins Neto, A. Cerveau, O.A. Calvo and L. Giraldo, Irreducible components of the
space of foliations associated to the affine Lie algebra, Ergodic Theory and Dynamical
Systems, 2003.
7. A. Lins Neto, Curvature of pencils of foliations, Atas do Cong. em homenagem J.P.
Ramis, 2003.
8. A. Lins Neto, On Halphen’s theorem and some generalizations, Annales de l’Institut
Fourier, 2003.
9. A. Lopes and P. Thieullen, Mather Theory and the Bowen-Series transformation, Ann.
Inst Henry Poincaré, Analise Nonlin, 2003.
10. A. Lopes and P. Thieullen, Subactions for sov Flows, Ergodic Theory and Dynamical
Systems, 2003.
11. A. Lopes and P. Thieullen, Subactions for,sov Diffeomorphisms, Asterisque, 287, 135146, 2003.
83
12. A. Lopes and R. Exel, C* Algebras, approximately proper equivalence relations and
Thermodynamic Formalism, Ergodic Theory and Dynamical Systems, 2, 327-338,
2003.
13. B. Scárdua and C.A. Morales, Geometry, dynamics and topology of foliated manifolds,
IMPA Mathematical Publications, 2003.
14. C. Bonatti and M. Viana, Lyapunov exponents with multiplicity 1 for deterministic
products of matrices, Ergodic Theory and Dynamical Systems, 2003.
15. C. Bonatti, C. Matheus; A. Wilkinson and M. Viana, Abundance of stable ergodicity,
Comentarii Math. Helvetici, 2003.
16. C. Bonatti, X. Gomez-Mont and M. Viana, Généricité d'exposants de Lyapunov nonnuls pour des produits déterministes de matrices, Ann. Inst. Henri Poincaré, An. NonLinéaire, 20, 579-624, 2003.
17. C. Carballo and C.A. Morales, Omega-limit sets close to singular-hyperbolic attractors,
Illinois J. Math., 2003.
18. C.A. Morales and M. J. Pacifico, A dichotomy for three-dimensional vector fields,
Ergodic Theory Dynamical Systems, 23, 1575-1600, 2003.
19. C.A. Morales and M.J. Pacifico, A dichotomy for three-dimensional vector fields,
Ergodic Theory and Dynamical Systems, 2003.
20. C.A. Morales and M.J. Pacifico, Sufficient conditions for robustness of attractors,
Pacific J. Math, 2003.
21. C.A. Morales and M.J. Pacifico, Sufficient conditions for robustness of attractors,
Pacific Journal on Mathematics, 2003.
22. C.A. Morales, 3-manifolds supporting, sov flows and abelian normal subgroups,
Topology Appl, 2003.
23. C.A. Morales, A note on periodic orbits for singular-hyperbolic Flows, Disc. &
Continuous Dynamical Systems, 2003.
24. C.A. Morales, Axiom A flows with a transverse torus, Trans. Amer. Math. Soc, 2, 735745, 2003.
25. C.A. Morales, M.J. Pacifico and B. San Martim, Expanding Lorenz attractors through
resonant double homoclinic loops, SIAM J. Math. Anal, 2003.
26. C.A. Morales, M.J. Pacifico and B. San Martim, Expanding Lorenz attractors through
resonant double homoclinic loops, SIAM on Mathematical Analysis, 2003.
27. C.A. Morales, Singular-hyperbolic sets and topological dimension, Dynamical
Systems, 181-189, 2003.
28. C.A. Morales, The explosion of singular-hyperbolic attractors, Ergodic Theory and
Dynamical Systems, 2003.
29. C.G. Moreira and A. Avila, Bifurcations of unimodal maps. Pubblicazioni del Centro de
Giorgi, Dynamical Systems, 1, 1-22, 2003.
30. C.G. Moreira and A. Avila, Quasisymmetric robustness of the Collet-Eckmann
condition in the quadratic family, 2003.
31. C.G. Moreira and A. Avila, Statistical properies of unimodal maps:smooth families with
negative Schwarzian derivative, Astérisque, 286, 81-118, 2003.
84
32. C.G. Moreira and A. Avila, Topological Geometrical and Ergodic Properties of
Dynamics, Pub. della C. di Scienze, Sc. N. Super, Pisa, 2003.
33. C.G. Moreira and A. Munoz, Sums of Cantor sets whose sum of dimensions is close to
one. Nonlinearity, Transactions of the AMS, 16, 1641-1647, 2003.
34. C. Gutierrez and A. Sarmiento, Injectivity of C1 Maps R2 ≥ R2 at infinity and Planar
Vector Fields, Astérisque, 287, 89-102, 2003.
35. C. Gutierrez and C. Oliveira, Almost Periodic Schrödinger Operators Along Interval
Exchange Transformations, Journal of Mathematical Analysis and Applications, 283,
570-581, 2003.
36. C. Gutierrez and M.A S. Ruas, Indices of Newton Non-Degenerate Vector Fields and a
Conjecture of Lowner for surfaces in R4, A Dekker Series of Lecture Notes in Pure and
Applied Mathematics, 232(12), 245-253, 2003.
37. C. Gutierrez and Nguyen Van Chau, Properness and the Jacobian Conjecture in R2,
Vietnam Journal of Mathematics, 31(4), 421-427, 2003.
38. C. Gutierrez and V. Guiñez, Simple Umbilic Points on Surfaces Immersed in R4,
Discrete and Continuous Dynamical Systems, 9, 877-900, 2003.
39. C.M. Carballo and C.A. Morales, Homoclinic classes and finitude of attractors for
vector fields on n-manifolds, Bulletin London Math. Soc., 1, 85-91, 2003.
40. C.M. Carballo, C.A Morales and M. J. Pacifico, Homoclinic classes for generic C1
vector fields, Ergodic Theory Dynamical Systems, 2, 403-415, 2003.
41. E. Colli and V. Pinheiro, Chaos versus renormalization at quadratic S-unimodal
Misiurewicz bifurcations, Astérisque, 1, 257-308, 2003.
42. E. de Faria, F. Gardiner and W. Harvey, Thompson's group as a Teichmüller mapping
class group, Systems Contemp. Math. (AMS), 2003.
flows, Procs. Amer.Math. Soc, 2003.
44. F. Abdenur, Attractors of generic diffeomorphisms are persistent, Nonlinearity, 1, 301311, 2003.
45. F. Abdenur, Generic robustness of spectral decompositions, Ann. Sci. Ecole. Norm.
Sup., 2, 213-224, 2003.
46. J. Bochi and M. Viana, Lyapunov exponents: how frequently are dynamical systems
hyperbolic, Adv. in Dyn. Systems, Camb. Univ. Press, 2003.
47. J. Bochi and M. Viana, Lyapunov exponents: How frequently are dynamical systems
hyperbolic, A. Katok Festschrift, Cambridge Univ., 355, 735-745, 2003.
48. J. Bochi and M. Viana, Pisa lectures on Lyapunov exponents, Dynamical Systems,
2003.
49. J. Bochi and M. Viana, Pisa lectures on Lyapunov exponents, Top. Geom. & Ergodic
Properties of Dyn., 2003.
50. J. Bochi and M. Viana, Pisa lectures on Lyapunov exponents, Topo. Geometrical &
Ergodic Prop. of Dyna., 2003.
51. J. Bochi and M. Viana, The Lyapunov exponents of generic volume preserving and
symplectic maps, Annals of Mathematics, 2003.
85
52. J. Bochi, Inequalities for numerical invariants of sets of matrices, Linear Algebra and
Applications, 368, 71-81, 2003.
53. J. Sotomayor and R. Garcia, A metric property of umbilic points, Anais da Academia
Brasileira de Ciências, RJ, 75(4), 405-413, 2003.
54. J. Sotomayor and R. Garcia, Structural Stability of Piecewise linear vector fields,
Journal of Differential Equations, 192(2), 553-565, 2003.
55. J. Sotomayor, C. Gutierrez and R. Garcia, Bifurcations of Umbilic Points and related
Principal Cycles, Journal of Dynamics and Differential Equations, 15, 1-26, 2004.
56. J. Sotomayor, L.F. Mello and R. Garcia, Principal Mean Curvature Foliations on
Surfaces immersed in R 4, In Equadiff-2003, Proceedings of Equadiff, 1-12, 2003.
57. J. Sotomayor, R. Garcia, Harmonic Mean Curvature Lines on Surfaces Immersed in
R3, Bull. Braz. Math. Soc., 34(2), 303-331, 2003.
58. L.J. Díaz and I Rios, Critical saddle-node horseshoes: bifurcations and entropy,
Nonlinearity, 3, 897-929, 2003.
59. L.J. Díaz and I Rios, Critical saddle-node horseshoes: bifurcations and entropy,
Nonlinearity, 16, 897-929, 2003.
60. L.J. Díaz, C. Bonatti and E.R. Pujals, A C1-generic dichotomy for diffeomorphisms:
Weak forms of hyperbolicity or infinitely many, sinks or sources Annals of
Mathematics, 158, 355-418, 2003.
61. L.J. Díaz, C. Bonatti and E.R. Pujals, A C1-generic dichotomy for diffeomorphisms:
Weak forms of hyperbolicity or infinitely many sinks or sources, Annals of
Mathematics, 2, 355-418, 2003.
62. L.J. Díaz, C. Bonatti, E.R. Pujals and J. Rocha, Robustly transitive sets and
heterodimensional cycles, Astérisque, 286, 187-222, 2003.
63. L.J. Díaz, C. Bonatti; E.R. Pujals and J. Rocha, Robustly transitive sets and
heterodimensional cycles, Astérisque, 286, 187-222, 2003.
64. M.A. Teixeira and A. Jacquemard, Computer analysis of periodic orbits of
discontinuous fields, Journal of Symbolic Computation, 35, 617-636, 2003.
65. M.A. Teixeira and A. Jacquemard, On singularities of discontinuous vector fields, Bull.
Sc. Matheamatiques, 127, 611-633, 2003.
66. M.G. Soares, Determination of the top Baum-Bott number via classical intereserction
theory, Bull. Braz. Math. Soc, 2003.
67. M.I. Camacho, C. Alonso and F. Cano, Topological Equivalence for Multiples Saddle
Connections, Academia Brasileira de Ciências, 74, 577-584, 2003.
68. M.I. Camacho, The topology of flows near a dicritical singularity, Journal of Diff.
Equations, 193, 261-279, 2003.
69. M.J. Dias Carneiro and R.O. Ruggiero, On variational an topological properties of C1
invariant Lagrangian tori, Ergodic Theory and Dynamical Systems, 2003.
70. M.J. Dias Carneiro, O.S. Kamphorst and S. Pinto Carvalho, Elliptic Islands on Strictly
Convex Billiards, Ergodic Theory and Dynamical Systems, 23, 799-812, 2003.
71. M.J. Pacifico, E.R. Pujals and J.L. Vieitez, Robustly expansive homoclinic classes,
86
72. P. Sad and J.V. Pereira, On the holonomy group of algebraic curves invariant by
holomorphic foliations, Annali della Scuola Normale Superiore, Ann. di Mat.Pura et
Aplicata, 2003.
73. P. Sad and D. Cerveau, Fonctions et Feuilletages Levi-flat. Étude locale, Annali della
Scuola Normale Superiore/Ann. di Mat. Pura et Aplicata., 2003.
74. P. Sad, C. Camacho and H. Movasati, Fibered Neighborhoods of Curves in Surfaces,
Journal of Geometric Analysis, 13, 2003.
75. S. Luzzatto and M. Viana, Parameter exclusions in Hénon-like systems, Russian Math.
Surveys, 1053-1092, 58, 2003.
76. W. de Melo, J.-C. Yoccoz and M. Viana, Geometric methods in Dynamics (I),
Asterisque, xxviii + 308, 286, 2003.
77. W. de Melo, J.-C. Yoccoz and M. Viana, Geometric Methods in Dynamics (II),
Asterisque, 287, xxii+272, 2003.
1. A. Arbieto and J. Bochi, Lp-generic cocycles have one-point spectrum, Stochastic and
Dynamics, 2002.
2. A. Avila and J. Bochi, A formula with some applications to the theory of Lyapunov
exponents, Israel Journal of Mathematics, 131, 125-148, 2002.
3. A. Avila, W. de Melo and M. Lyubich, Regular or Stochastic Dynamics in Real Analytic,
Inventiones Mathematicae, 2002.
4. A. Lins Neto, Some examples for Poincaré and Painlevé problems, Ann. Scientifiques
de l’École Norm. Supér, 35, 231-266, 2002.
5. A. Lopes and S. Lopes, Convergence in distribution of the periodogram of chaotic
systems, Stochastics and Dynamics, 4, 2002.
6. A. Lopes, Subactions for, sov Diffeomorphisms, Astérisque, 2002.
7. C. Alonso, M.I. Camacho and F. Cano, Topological equivalence for multiple saddle
connections in dimension three, Anais da Academia Brasileira de Ciências, 2002.
8. C. Bonatti and M. Viana, Lyapunov exponents with multiplicity 1 for deterministic
products of matrices, Ergodic Theory and Dynamical Systems, 2002.
9. C. Bonatti, L.J. Díaz and E.R. Pujals, A C1 generic dichotomy for diffeomorphisms:
weak of forms of hyperbolicity or infinitely many sinks or sources, Annals of
Mathematics, 2002.
10. C. Bonatti, L.J. Díaz and R. Ures, Minimality of the strong foliations for partially
hyperbolic diffeomorphisms, J. de l'Inst. de Mathématiques de Jussieu, 2002.
11. C. Bonatti, L.J. Díaz, E.R. Pujals and J. Rocha, Robustly transitive sets and
heterodimensional cycles, Astérisque, 2002.
12. C. Bonatti, X. Gomez-Mont and M. Viana, Généricité d'exposants de Lyapunov nonnuls pour des produits deterministes de matrices, Annales Inst. Henri Poincaré, 2002.
13. C. Camacho, H. Movasati and P. Sad, Fibered neighborhoods of curves in surfaces,
The Journal of Geometric Analysis, 13, 2002.
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14. C. Gutierrez and J. Llibre, Darbouxian integrabililty for polynomial vector fields on the
2-dimensional sphere, Extracta Mathematicae, 13, 289-301, 2002.
15. C. Gutierrez, Jaume Llibre and Milton Cobo, On the injectivity of C1 maps of the real
plane, Canad. J. Math. Canadá, 54, 1187-1201, 2002.
16. C.A. Morales and M.J. Pacifico, A dichotomy for three dimensional vector fields,
17. C.A. Morales and M.J. Pacifico, Lyapunov stability of omega-limit sets, Disc. and
Continuous Dynamical Systems, 8, 671-674, 2002.
18. C.A. Morales, Axiom A flows with a transverse torus, Transactions of the AMS, 355,
735-745, 2002.
19. C.A. Morales, M.J. Pacifico and E.R. Pujals, Robust transitive sets for 3-flows are
partially hyperbolic attractors or repellers, Annals of Mathematics, 2002.
20. C.G. Moreira and A. Avila, Statistical properies of unimodal maps: smooth families with
negative Schwarzian derivative, Astérisque, 2002.
21. C.G. Moreira and A. Avila, Statistical properties of unimodal maps: the quadratic
family, Annals of Mathematics, 2002.
22. C.G. Moreira and Y. Kohayakawa, Bounds for Optimal Coverings, Discrete Applied
Mathematics, 2002.
23. C.G. Moreira, Introdução à Teoria dos Números, Monografias del IMCA, 250, 2002.
24. C.M. Carballo and C.A. Morales, Homoclinic classes and finitude of attractors for
vector fields on n-manifolds, Bull. London Math. Soc., 35, 85-91, 2002.
25. C.M. Carballo, C.A. Morales and M.J. Pacifico, Homoclinic classes for generic C1
vector fields, Ergodic Theory and Dynamical Systems, 2002.
26. E. Colli and V. Pinheiro, Chaos versus renormalization at quadratic S-unimodal
Misurewicz bifurcations, Astérisque, 2002.
27. E. de Faria, Aspects of rigidity and universality in one-dimensional dynamics, Fields
Institute Communications, 31, 113-123, 2002.
28. E. de Faria, F. Gardiner and W. Harvey, Thompson's group as a Teichmueller
mapping class group, Conteporary Mathematics, 2002.
29. E.R. Pujals, Tangent bundle dynamics and its consequences, Procs. Intern. Congres
of Mathematicians, 2, 327-338, 2002.
flows, Proceedings of the AMS, 16, 301-311, 2002.
31. F. Abdenur, Attractors of generic diffeomorphisms are persistent, Nonlinearity, 2002.
32. F. Abdenur, Generic robustness of spectral decompositions, Annales Scientifiques de
l'ENS, 2002.
33. J. Bochi and M. Viana, Lyapunov exponents: How often are dynamical systems
hyperbolic, Advances in Dynamical Systems, 2002.
34. J. Bochi and M. Viana, Uniform (projective) hyperbolicity or no hyperbolicity, Annales
de l'Inst. Henri Poincaré, 19, 113-123, 2002.
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35. J. Bochi, Genericity of zero Lyapunov exponents, Ergodic Theory and Dynamical
Systems, 22, 1667-1696, 2002.
36. J. Bochi, Inequalities for numerical invariants of sets of matrices, Linear Algebra and
its Applications, 2002.
37. J. Palis, Chaotic and complex systems, Current Science, 82, 403-406, 2002.
38. J. Sotomayor and A.L.F. Machado, Structurally Stable Discontinuous Vector Fields in
the Plane, Qualitative Theory of Dynamical Systems, 3, 227-250, 2002.
39. J. Sotomayor and R. Garcia, Geometric Mean Curvature on Surfaces Immersed in R3,
Annales de la Faculté des Sciences de Toulouse, França, 11(3), 377-401, 2002.
40. J. Sotomayor and R. Garcia, Umbilic and Tangential Singularities on Configurations of
Principal Curvature Lines, Anais da Academia Brasileira de Ciências, RJ, 74(1), 1-17,
2002.
41. J. Sotomayor, J. Llibre and M. Zhitomirskii, Impasse Bifurcations of Constrained
Systems, Fields Institute Communications, 31, 235-255, 2002.
42. J.F. Alves and M. Viana, Statistical stability for a robust class of maps with non-uniform
expansion, Ergodic Theory and Dynamical Systems, 22(1), 1-32, 2002.
43. J.V. Pereira and P. Fernandez, Transformation groups of holomorphic foliations,
Communications in Anal. and Geometry, 2002.
44. J.V. Pereira, GLobal stability for holomorphic foliations on Kaehler manifolds,
Qualitative theory of dynamical systems, 2002.
45. J.V. Pereira, Integrabilidade de equações diferenciais no plano complexo,
Monografias del IMCA, 2002.
46. J.V. Pereira, Invariant hypersurfaces for positive characteristic vector fields, Journal of
Pure and Applied Algebra, 171, 295-301, 2002.
47. J.V. Pereira, On the Poincaré problem for foliations of general type, Mathematische
Annalen, 323, 217-226, 2002.
48. L.G. Mendes and P. Sad, Dicritical foliations and Halphen pencils, Ann. della Scuola
Normale Sup. di Pisa, 1, 2002.
49. L.J. Díaz and I.L. Rios, Critical saddle-node horseshoes: bifurcations and entropy,
Nonlinearity, 2002.
50. L.J. Díaz and J. Rocha, Heterodimensional cycles, partial hyperbolicity and limit
dynamics, Fundamenta Mathematicae, 127-186, 174, 2002.
51. L.J. Díaz and R. Ures, Critical saddle-node cycles: Hausdorff dimension and
persistence of tangencies, Ergodic Theory and Dynamical Systems, 22, 1117-1140,
2002.
52. M.A. Teixeira and A. Jacquemard, A note on rigid decompositions of reversible
mappings, Fields Institute Communications, 31, 189-199, 2002.
53. M.A. Teixeira and A. Jacquemard, Effective algebraic geometry and normal forms of
reversible mappings, Revista Mat. Complutense, 15, 31-55, 2002.
54. M.A. Teixeira and E.A. Silva, Global asymptotic stability on Euclidean spaces,
Nonlinear Analysis - TMA, 50(1), 91-114 2002.
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55. M.A. Teixeira and J.R. Medrado, Codimension-two singularities of reversible vector
fields in 3D, Qualitative Theory of Dynamical Systems J., 2(2), 399-428, 2002.
56. M.G. Soares, Determination of the top Baum-Bott number via classical intersection
theory, Boletim da Soc. Brasileira de Matemática, 2002.
57. M.G. Soares, Lectures on point residues, Monografias del IMCA, 2002.
58. M.I. Camacho, The topology of flows near a dicritical singularity, Journal of Differential
Equations, 2002.
59. M.J. Dias Carneiro and R.O. Ruggiero, On variational and topological properties of C1
invariant tori, Ergodic Theory and Dynamical Systems, 2002.
60. M.J. Dias Carneiro, S.O. Kamphorst and S.P. de Carvalho, Elliptic islands for strictly
convex billiards, Ergodic Theory of Dynamical Systems, 2002.
61. W. Colmenárez and C.A. Morales, Transverse surfaces and attractors for 3-flows,
Transctions of the Amer. Math. Soc., 354, 795-806, 2002.
Human Resources - 2004
1. Alexander Arbieto. Doutor. “Tópicos em Sistemas Conservativos e Problemas
Correlatos”. Marcelo Viana
2. Carlos Matheus. Doutor. “Contribuições a Teoria Ergódica de Sistemas não
Hiperbólicos”. Marcelo Viana
1. Aldo Portel Almada. Doutor. Conjuntos de Cantor regulares de S1 e minimalidade.
Edson de Faria
2. Alexandre Soares. Doutor. Ações e Geometria Transversa das Folheações
Holomorfas em R n e C 2. Carlos Morales
3. Elismar R. Oliveira. Mestre. Seqüências Kneading e classificação de aplicações
monótonas por partes. Artur Lopes
4. Flávia Malta Branco. Doutor. Subação para aplicações unidimensionais. Artur Lopes
5. Gilcione Nonato Costa. Doutor. “Folheações holomorfas com conjunto singular de
dimensão 1. Marcio G. Soares
6. Joana Mohr. Mestre. Conjuntos minimais para métricas Riemannianas no toro
bidimensional. Artur Lopes
7. Joseph Nee Anyah Yartey. Doutor. Generic Webs on the complex projective plane.
Alcides Lins neto
8. Josué Geraldo Damasceno. Mestre. Estruturas rígidas e flexíveis. Márcio G. Soares
9. Magali Smaniotto. Mestre. Análise Global de certas equações dos circuitos elétricos.
Artur Lopes
10. Márcio Alves. Mestre. Condições geométricas para caoticidade. Eduardo Colli
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11. Mychelle Dysman. Doutor. “Hausdor dimension of repellers of maps with holes.
Marcelo Viana
12. Rafael Souza. Doutor.
hiperbólicos. Artur Lopes
Subações
de
sistemas
um-dimensionais
fracamente
13. Regina Radicchi. Mestre. Equações diferenciais singulares, classificação topológica
em dimensão três. Mario Jorge D. Carneiro.
14. Serafin Bautista. Doutor. Sobre conjuntos hiperbólicos singulares. Carlos Morales
1. Ali Tahzibi. Doutor. Stably ergodic systems which are not partially hyperbolic. Jacob
Palis
2. Christiano Garcia. Mestre. O teorema de Denjoy. Artur Lopes
3. Clementa Alonso. Doutor. Topological equivalence for saddle connections. Maria
Izabel Camacho
4. Enoch Humberto Apaza. Mestre. Existência de pontos fixos comuns para
difeomorfismos comutativos. Maria José Pacifico
5. Flávio Abdenur. Doutor. Isolated transitive sets of C 1 generic systems. Marcelo Viana
6. German Aubin Arroyo. Doutor. Homoclinic bifurcations and uniform hyperbolicity for 3dimensional flows. Jacob Palis
7. João Pedro Pinto dos Santos. Mestre. Métodos analíticos na teoria da transcendência.
Carlos Gustavo Moreira
8. Krerley Irraciel Oliveira. Doutor. Equilibrium states for non-uniformly hyperbolic
systems. Marcelo Viana
9. Leonardo Meireles Camara. Doutor. Non-linear analytic differential equations and their
invariants. Alcides Lins Neto
10. Lineia Schutz. Mestre. Dinâmica de uma família de aplicações unimodais. Artur Lopes
11. Marcelo Sobotka. Mestre. Propriedades ergódicas do algoritmo da raiz quadrada. Artur
Lopes
12. Simone Dias Cruz. Doutor. Uma generalização da aplicação de Gauss e de alguns
teoremas clássicos sobre frações contínuas. Artur Lopes
13. Wilmer Colmenárez. Doutor. Sobre propriedades dinâmicas de atratores hiperbólicos
singulares. Maria Jose Pacifico
Other Activities
Events
1. Workshop Brasileiro de Física Matemática. Coordenador: Marcelo Viana. IMPA – Rio
de Janeiro, 3-5 de março 2004
2. I Reunião Regional de Sistemas Dinâmicos da UNESP. Coordenador: Vanderlei
Horita. UNESP – São Paulo, 26-28 de maio 2004
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3. International Worshop on Robustness and Partial Hyperbolicity. Coordenador: Marcelo
Viana. Búzios – Rio de Janeiro, 2-8 de novembro 2003
4. Congresso Internacional Qualitative Theory of Differential Equations. Coordenador:
Carlos Gutierrez. USP – São Carlos, 17-21 de junho 2002
Cooperation – A sample
1. Yosef Yomdin. Coordenador: Jacob Palis. IMPA – Rio de Janeiro. 15 de agosto-4 de
setembro de 2004.
2. Antonio Galves. Coordenador: Artur Lopes. UFRGS – Rio Grande do Sul, 3 dias em
2004.
3. Eugene Neduv. Coordenador: Marcelo Viana. IMPA – Rio de Janeiro. 5 meses em
2002.
4. Gonzalo Conteras. Coordenador: Artur Lopes. IMPA – Rio de Janeiro, 1-30 de outubro
de 2002.
Fellowships
Alexander Arbieto. Coordinator: Marcelo Viana. IMPA – Rio de January, 1 de June-31 de
December de 2004.
Emalca, Bolívia. Coordinator: Marcelo Viana. Cochabamba, Bolivia, 31 de May-12 June
de 2004. Mini-courses were delivered by Carlos Gustavo Moreira, Bernardo San Martin
and Luciano Irineu de Castro Filho.
Research visitors from main Latin American countries to several Brazilian institutions and
more than ten joint researches work published and several others under way.
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Topology and Singularity Theory
The promotion of the AGIMB Millenium Institute of the last two Brazilian Topology
Meetings in August 2002 and July 2004 contributed greatly to the development and
scientific productivity in topology in Brazil. In 2004 the Fourteenth Brazilian Topology
Meeting (XIV EBT) brought together the largest number of participants in these meetings
since they began in 1979. The realization of this meeting by the IM-AGIMB produced an
intense interchange of recent results with presentation of research of graduate students
and recent doctors, an important new achievement, since many research-funding agencies
do not finance the participation of doctoral students in scientific meetings. This support of
the Institute of the Millenium fills a serious gap and shows a wise long-term vision that
invests in the future of young researchers. The IM-AGIMB offers these students who are
working on the frontier of current research an early opportunity to present their work to the
scientific community in their area. There was also extensive interchange with the
international research community in topology, not only during the two Brazilian Topology
Meetings, but also throughout these 30 months.
The flexibility of the IM and its commitment to main research activities allowed long-range
planning and consequently a more efficient use of the funds. There is a multiplying effect,
since if another funding agency fails to offer support at the last minute, the event can be
realized with support of the IM.
The Fourteenth Brazilian Topology Meeting demonstrated a very positive evolution in the
Brazilian research community in topology in recent years. The lectures delivered spanned
a wider variety of relevant subjects in current topological research than two or four years
ago. Furthermore, there was a clear growth in the number of senior topologists among the
Brazilian speakers.
At the Mathematics and Statistics Institute of the University of São Paulo (IME-USP), there
were substantial advances in coincidence theory for manifolds of different dimensions. The
study of braids in surfaces also had significant progress, as in the aspects related to
sequences of Fadell-Neuwirth type. The study of topological dynamical systems advanced
at Unicamp. At the Federal Fluminense University (UFF) there was a substantial
improvement in the quality and quantity of scientific papers produced. At PUC-Rio there
was significant progress in the study of the geometry and dynamics of real and complex
foliations. The current visit of Dr. Miguel Bermúdez at PUC-Rio, with post-doctoral support
from the IM, is extending this work to foliations which are only measurable in the
transverse direction.
Support of the IM-AGIMB certainly contributed to the major qualitative and quantitative
improvement of Brazilian Topology since 2002. Some papers which are especially
significant for the advancement of the area in this period are:
1. F. Dutenhefner, N. Gusevskii, Complex hyperbolic Kleinian groups with limit set a wild
knot. Topology, 43(3), 677-696, 2004.
2. Daciberg L. Gonçalves and John Guaschi, On the structure of surface pure braid
groups, Journal of Pure and Applied Algebra, 186, 187-218, 2004.
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3. J.C.S. Rebelo; Complete algebraic vector fields on affine surfaces, Part II. J. Diff.
Equations, 1-37, 2003.
4. P.L.Q. Pergher, D. de Mattos and E. L. dos Santos; The Borsuk-Ulam theorem for
general spaces. Archiv Der Mathematik, 81(1), 96-102, 2003.
5. M.A. Bertolim, M.P. Mello and K.A. de Rezende; Lyapunov Graph Continuation:
Ergodic Theory and Dynamical Systems, 23, 1-58, 2003.
6. P.A. Schweitzer, S.J.; Homological vanishing cycles and existence of Reeb
components for codimension one foliations; Geometry and Foliations Kyoto, Abstracts,
404-410, 2003.
7. S. Druck, F. Fang and S. Firmo, Fixed points of discrete nilpotent groups actions on
S2, Ann. Inst. Fourier, 52(4), 1073-1089, 2002.
8. R. O. R. Rodriguez; An introduction to the study of variational and topological aspects
of invariant tori of the geodesic flow of surfaces; Monografia, Instituto de Matemática y
Ciencias Afines (IMCA), Lima, Peru, 2002.
Singularity Theory
During the period 2002-2004, the singularity group achieved important developments in
the following directions: (1) classification and recognition of singularities and the study of
their topology and associated invariants; (2) generic properties of submanifolds in
Euclidean spaces; (3) methods of singularity theory in bifurcation problems; (4) metric
theory of singularities. For complex singularities, the main results are new formulas for
invariants associated to a large class of finitely-determined map-germs. Our results also
lead to a better understanding of real singularities for which the topology of their maximal
stabilizations resembles that of its complexification. In an ongoing project of our research
group on generic properties of surfaces in Euclidean spaces using singularity theory and
implicit differential equations, new results on the local geometry of surfaces in R4 and R5
were obtained.
The results we obtained were published in 39 papers and two books. Among them, the
most relevant to the progress of the area are:
1. J. Rieger and M.A.S. Ruas, M-deformations of A-simple Sigma n-p+1-germs from Rn to
Rp, n ≥ p, Math. Proc.Cambridge Phil. Soc., 2005.
2. D. Levcovitz, V.H. Jorge Perez and M.J. Saia, Euler obstructions and equisingularity,
J. für die reine und ang. Math., 2004.
3. C. Bivià-Ausina, T. Fukui and M.J.Saia, Newton filtrations, graded algebras and the
codimension of ideals, Math. Proc. Cambridge Philos. Soc., 133, 55-75, 2002.
4. T. Cooper, D. Mond and R. Wik Atique, Vanishing Topology of codimension 1 multigerms over R and C, Compositio Mathematica, 131, 121-160, 2002.
5. J.W. Bruce and F. Tari, Families of surfaces in R 4, Proc. Edinb. Math. Soc., 45(2), 181203, 2002.
The partnership with the IM-AGIMB allowed us to successfully organize international
workshops and supported several scientific visits of researchers from other countries to
São Carlos. The scientific interchange was an important factor to intensify our
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postgraduate program: the group supervised 6 PhD thesis during the period 2002-2004,
and presently has 13 PhD students, which corresponds to 40% of all PhD students of the
ICMC-USP. The effects of the partnership with IM-AGIMB extend to the associated
institutions, for instance, IBILCE-UNESP and Universidade Federal do Ceará, which had a
good record of scientific publications during the period.
The excellent scientific progress of the group during these last 30 months was to a large
extent due to the IM-AGIMB: being part of this virtual institute of excellence, with other
leading Brazilian mathematicians, the possibility of planning the activities of the group, and
promoting them in a very flexible way were determining factors in the progress of the
singularity group in São Carlos and of other associated centers. The importance of the IMAGIMB to the progress of the area can be seen from the activities we report below.
Our group is proud of organizing one of the most influential workshops in the area. The
biannual series “Workshop on Real and Complex Singularities” started in 1990, and has
become a key international event for people working in singularity theory and its
applications. This event allowed members of our group to increase collaborative work with
leading researchers in the field and to spread research in singularity theory to various
universities in Brasil. The VIIth workshop held in July 2002, had 118 participants, 44 from
other countries, 74 from Brasil and among them, 45 were students. The support of the IMAGIMB was very important for the success of the meeting. Some participants from abroad
extended their stay in São Carlos or visited other universities, extending the benefits of the
interchange to newly formed singularity groups in other universities. Among them: A. Jeddi
(Nancy), A. Pichon (Marseille), J. Rieger (Halle), C. Bivià-Ausina (València), J. E. Furter
(Brunel), M. C. Romero-Fuster (València), J. W. Bruce (Liverpool). The papers presented
at the VII workshop are being published in Real and Complex Singularities, Contemporary
Mathematics, v. 354, AMS, 2004, edited by T. Gaffney and M.A. S. Ruas.
The visit of Ana Paula Dias, also supported by the IM-AGIMB, was part of a more than 10
years of interchange between the Brazilian group and researchers from the Universidade
do Porto, Portugal. As part of the activities of her visit, she taught a short course on
applications of singularity theory to bifurcations. Some researchers from the Physics
Institute, USP/São Carlos also attended the lectures. The article “Bifurcation problems and
coupled hemispheres” by Ana Paula Dias and Miriam Manoel is in progress.
Jonathan Schewchuk from Berkeley, USA, visited Brazil during the period of 1 to 11
September 2002. During his stay, he visited the ICMC-USP, PUC/RJ, IMPA, and IbilceUnesp/Rio Preto. The PhD thesis "Triangulação de Delaunay anisotrópica" of Igor Prata
Soares, ICMC-USP, had an important influence from Shewchuk's visit, and the student will
visit Berkeley next year to continue the interchange.
Farid Tari's visit is in progress. Prof. Tari had a position at the ICMC-USP from June 1996
to July 2003, and he has now a position at the University of Durham, England. While he
lived in São Carlos, he was the supervisor of 3 PhD students. One of the aims of the
present visit is to continue his joint work with his former students and other local
researchers. He is also the co-supervisor of the PhD thesis of Lizandro Challapa, on
indices of binary equations.
Alicia Dickenstein, a well-known specialist in real algebraic geometry and computer
algebra from the University of Buenos Aires, visited the ICMC- USP, São Carlos, from
February 2 to 20, 2004. During her stay, she taught a short course on “Discriminants,
95
resultants and multidimensional discriminants”, based on the book by Gelfand, Kapranov
and Zelevinsky (Ed. Birkhauser, 1994). The visit occurred during our summer program and
researchers from IBILCE-UNESP, UFCe and UFSCar also attended the lectures. The visit
started an interesting interchange with South American researchers, which may contribute,
to improving our results on real algebraic singularities.
The partnership with the IM-AGIMB was important to improve our Postdoc Program: the
postdoctoral researchers Fuensanta Aroca and Jawad Snoussi are currently supported by
IM-AGIMB. During this period, they published the papers Aroca, F.; Puiseux parametric
equations of analytic sets, in Proceedings of the American Mathematical Society, 132:
3035-3045, 2004, and Aroca, F. and Snoussi, J.; Normal Quasi-ordinary singularities, to
appear in Seminaires et Congrès, Société Mathematique de France.
Theses in Topology and Singularities 2002-2004
1. Ana Lucia da Silva, Sobre o problema de Burnside em Diff (M). ICMC-USP, 2004.
Advisor: Julio Cesar de Souza Rebelo
2. José Barbosa Gomes, Rigidez de superfícies cujos fluxos geodésicos preservam
folheações de codimensão um, PUC-Rio, 29/01/2004. Advisor: Rafael Oswaldo
Ruggiero Rodríguez.
3. Marcelo Buosi, Imersões horojustas em espaços hiperbólicos, ICMC-USP, prevista
para setembro de 2004. Advisor: Maria Aparecida Soares Ruas
4. Carlos Humberto Soares Junior, Poliedros de Newton e trivialidade em famílias de
aplicações. ICMC-USP, maio de 2003. Advisor: Marcelo José Saia
5. Jose Carlos de Sousa Junior, Aneis d-simples e ideais maximais da algebra de Weyl,
ICMC-USP, fevereiro de 2003. Advisor: Daniel Levcovitz
6. Liane Mendonça Feitosa, Trivialidade topológica de germes pre quase homogêneos.
ICMC-USP, agosto de 2003. Advisor: Marcelo José Saia
7. Luciana de Fátima Martins Brito, Folheações Singulares em D2 x S1. ICMC-USP,
2003. Advisor: José Luis Arraut Vergara.
8. Luís Fernando Crocco Afonso, Representações de grupos triangulares em geometria
hiperbólica complexa, PUC-Rio, 29/08/2003. Co-Advisor: Nikolai Goussevskii e Paul
A. Schweitzer.
9. Seme Gebara Neto, Domínios fundamentais de Ford para grupos discretos de
isometrias hiperbólicas complexas, UFMG, 11 de dezembro de 2003. Advisor: Nikolai
Goussevskii.
10. Alexandre Cesar Gurgel Fernandes, Teoria métrica de curvas complexas. ICMC-USP,
27/03/2002. Advisor: Maria Aparecida Soares Ruas
11. Carlos Alberto Maquera Apaza, Ações de Rn em Mm com 2 = n = m = 3, ICMC-USP,
2002. Advisor: José Luis Arraut Vergara.
12. Claudemir Aniz, Índice de Classes de Coincidências em Superfícies; ICMC-USP,
12/09/2002. Advisor: Daciberg Lima Gonçalves.
13. Daniel Vendrúsculo, Teoria de coincidência equivariante e números de Nielsen
equivariante. IME-USP, 25/04/2002. Advisor: Daciberg Lima Gonçalves.
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14. Francisco Dutenhefner, Representacões de Grupos Fuchsianos no Espaço
Hiperbolico Complexo, UFMG, 21 de junho de 2002. Advisor: Nikolai Goussevskii.
15. Leonardo Navarro de Carvalho, Automorfismos genéricos de cubos com alças, PUCRio, 01/11/2002. Co-Advisor: Paul A. Schweitzer e Ulrich Oertel.
16. Magno Branco Alves, Sobre redução de singularidades de fluxos holomorfos em
dimensão três, PUC-Rio, 25/03/2002. Advisor: Julio Cesar Rebelo.
17. Marcos Martins Alexandrino da Silva, Folheações riemannianas singulares com
seções e aplicações transnormais, PUC-Rio, 23/09/2002. Co-Advisor: Ricardo Sá
Earp e Gudlaugur Thorbergsson.
18. Maria Alice Bertolim, Grafos de Lyapunov, desigualdades de Poincaré-Hopf e de
Morse, ICMC-USP, 2002. Co- Advisor: Ketty Rezende e Ozíride Manzoli Neto.
19. Raimundo Nonato Araujo dos Santos, Fibrações de Milnor Reais. ICMC-USP, 25/05/
2002. Advisor: Maria Aparecida Soares Ruas
20. Rogério de Oliveira, Involuções comutante fixando dois espaços projetivos pares,
UFSCar, 2002. Advisor: Pedro Luiz Pergher.
21. Simone Maria de Moraes, Elipses de curvatura em superfícies imersas no Rn.
IMECC-UNICAMP, fevereiro de 2002. Advisors: Sueli Irene Rodrigues Costa e aria del
Carmen Romero Fuster
Publications of Research Articles and Books
1. D.L. Gonçalves and C. Aniz, The minimizing of the Nielsen root classes, Central
European Journal of Mathematics, 2(1), 112-122, 2004.
2. D.L. Gonçalves and J. Guaschi, On the structure of surface pure braid groups, Journal
of Pure and Applied Algebra, 186, 187-218, 2004.
3. D.L. Gonçalves, S. Bogatyi, H. Zieschang and E. Kudryavtseva, Minimal number of
roots of surface mappings, Math. Zametki, 75(1), 13-19, 2004.
4. F. Dutenhefner and N. Gusevskii, Complex hyperbolic Kleinian groups with limit set a
wild knot. Topology, 43(3), 677-696, 2004.
5. J.C.S. Rebelo, Meromorphic vector fields and elliptic fibrations, Mich. Math. Journal,
52, 33-59, 2004.
6. J.C.S. Rebelo, Vertical vector fields on certain complex fibrations. Journal of
Mathematical Sciences, University of Tokyo, 1-67, 2004.
7. M.M. Alexandrino, Integrable riemannian submersion with singularities, Geom.
Dedicata, 2004.
8. M.O.M. da Silva, N.S.Cardim, D. Randall, M.A.P.L.Mello, Join products and indices of
k-fields over differentiable fiber bundles, Topol. and its Applications, 136(1-3), 275291, 2004.
9. N.E. Barufatti, D. Hacon, K.Y. Lam, P. Sankaran and P. Zwengrowski, The order of
real line bundles, Bol. Soc. Mat. Mexicana (3a série), 10(1), 149-159, 2004.
10. P. Gusmão P, A Sarmiento, Foliations on 3-manifolds which are the classifying space
of themselves, Bull. Braz. Math. Soc., 35, 1-15, 2004.
97
11. P.A. Schweitzer, S.J. and P. Walczak, Prescribing mean curvature vectors for
foliations, Illinois J. Math., 48, 21-35, 2004.
12. B. Scárdua and C. Morales, Geometry, Dynamics and Topology of Foliated Manifolds,
IMPA, 2003 (240 Colóquio Brasileiro de Matemática).
13. C. Biasi, A K. Libardi, Remarks on Immersions in Metastable Dimension Range. Proc.
Edinburgh Mathematical Society, 2003.
14. C. Biasi, J.Àlvarez López and J.L. Arraut, Foliations by planes and Lie Group actions,
Annales Polonici Math., 82(1), 61-69, 2003.
15. C. Gutierrez and A Sarmiento, Injectivity of C1 maps R2 to R2 at infinity and planar
vector field. Astérisque, 287, 89-102, 2003.
16. D.L. Gonçalves and J. Guaschi, On the structure of the braids group, Journal of Pure
and Applied Algebra, 182(1), 33-64, 2003.
17. D.L. Gonçalves and L.D. Borsari, Obstruction Theory and coincidences from a
complex into a manifold. TMNA-Topological Methods in Nonlinear Analysis, 21, 115130, 2003.
18. D.L. Gonçalves and M. Golasinski, Spherical space forms -homotopy types and selfequivalences. Progress in Mathematics (The Skye Conference Proceedings), 215,
153-165, 2003.
19. D.L. Gonçalves and M. Kelly, Connectivity properties for subspaces of C(Sk)
determined by the fixed points, Abstract and Applied Analysis, (Proc. of the Israel
conference), 2, 121-128, 2003.
20. D.L. Gonçalves and Peter Wong, Twisted conjugacy classes in exponential growth
groups, Bulletin of the London Mathematical Society, 35, 261-268, 2003.
21. D.L. Gonçalves, S. Bogatyi, H. Zieschang and E. Kudryavtseva, On the Wecken
property of continuous mappings between surfaces, Mathematical Journal, 3(4), 12231245, 2003.
22. D.L.Gonçalves, S. Bogatyi, H. Zieschang and E. Kudryavtseva, Construction of
Branched Coverings over Closed Surfaces Following the Hurwitz Approach, Central
European Mathematical Journal, 2, 184-197, 2003.
23. F. Cardona and P. Wong, The relative Reidemeister numbers of fiber map pairs,
Topological Methods in Nonlinear Analysis, Journal of the Julius Schauder Center, 21,
131-145, 2003.
24. G. Tavares, H. Lopes, A.W. Vieira and T. Lewiner, Efficient implementation of
matching cube cases with topological guarantees, Journal of Graphics Tools, 28, 1-15,
2003.
25. H. Lopes, J. Rossignac, A. Safanova, A. Szymczac and G. Tavares, Edgebreaker, A
simple implementation for surfaces with handles; Computers and Graphics 27, 553567, 2003.
26. J. C. Rebelo; Complete algebraic vector fields on affine surfaces, J. Geometric Anal.
13, 669-696, 2003.
27. J.C.S. Rebelo and F. Loray, Minimal, rigid foliations by curves on CP(n), J. European
Math. Soc., 5, 147-201, 2003.
98
28. J.C.S. Rebelo, Complete algebraic vector fields on affine surfaces, Part I. Journal of
Geometric Analysis, 13(4), 669-696, 2003.
29. J.C.S. Rebelo, Complete algebraic vector fields on affine surfaces, Part II. J. Diff.
Equations, 1-37, 2003.
30. J.C.S. Rebelo, Subgroups of Diff (S1) acting transitively on 4-tuples, Trans. of the
AMS, 2003.
31. M.A. Bertolim, M.P. Mello, K.A. de Rezende, Lyapunov Graph Continuation, Ergodic
Theory and Dynamical Systems, 23, 1-58, 2003.
32. M.O.M. da Silva and M.A.P.L.Mello, Splitting 3-plane sub-bundles over the product of
two real projective spaces, Bol. da Soc. Paranaense de Matemática. SPM/UEM, 21(12), 43-50, 2003.
33. N. Gusevskii, J.R. Parker, Complex hyperbolic quasi-Fuchsian groups and Toledo's
invariant. Special, volume dedicated to the memory of Hanna Miriam Sandler (19601999). Geom. Dedicata, 97, 151-185, 2003.
34. P. Andrade and S. Firmo, Foliations which are limit of isotopic fibrations, Topology
Appl., 130(3), 205-219, 2003.
35. P.A. Schweitzer, S.J., Homological vanishing cycles and existence of Reeb
components for codimension one foliations; Geometry and Foliations Kyoto 2003,
Abstracts, 404-410.
36. P.L.Q. Pergher, A Zp-Index homomorphism for Zp-Spaces, Houston J. of Math., 2003.
37. P.L.Q. Pergher, D. de Mattos, E.L. dos Santos, The Borsuk-Ulam theorem for general
spaces, Archiv Der Mathematik, 81(1), 96-102, 2003.
38. R.O.R. Rodriguez, On the divergence of geodesic rays in manifolds without conjugate
points, dynamics of the geodesic flow and global geometry, Astèrisque, 287, 2003.
39. R.O.R. Rodriguez, V.R. Meneses, On the Pesin set of expansive geodesic flows in
manifolds without conjugate points, Bol. Soc. Bras. de Mat., 34(2), 263-274, 2003.
40. S. Druck and S. Firmo, Periodic leaves for diffeomorphisms preserving codimension
one foliations, Journal of the Mathematical Society of Japan, 55(1), 13-37, 2003.
41. T. Lewiner, H. Lopes and G. Tavares, Optimal discrete Morse functions for 2manifolds, Comp. Geom. Theory and Appls., 26, 221-233, 2003.
42. T. Lewiner, H. Lopes and G. Tavares, Toward optimality in discrete Morse theory,
Experimental Math., 12, 271-285, 2003.
43. C. M. de Jesus and M. C. Romero-Fuster, Bridges, channels and Arnold’s invariants
for generic plane curves. Top. Appls. 125, 505-524, 2002.
44. D. L. Gonçalves, H. Zieschang and E. Kudryavtseva, Roots of maps on non-orientable
case and equation on free groups, Manuscripta Mathematica, 107(3), March, 311-342,
2002.
45. D. L.Gonçalves, P. Pergher and J. Jaworowski, Measuring the size of the coincidence
set, Topology and its Application, 125 (3), 465-470, 2002.
46. D.L. Gonçalves and J. Peres Vieira, Infra-abelian groups and free actions of finite
groups on the n-torus-Comm. in Algebra, 30(6), 2791-1803, 2002.
99
47. D.L. Gonçalves and M. Kelly, Maps into the torus and minimal coincidence sets for
homotopies, Fundamenta Mathematicae, 172, 99-106, 2002.
48. D.L. Gonçalves and P.S. Wong, Factorization of groups homomorphism, Journal of
Pure and Applied Algebra, 171, 198-204, 2002.
49. D.L. Gonçalves, P., Pergher and J. Jaworowski, G-coincidences for maps of homotopy
sphere into CW-coplexes, Proc. of the American Mathematical Society, 130(10), 31113115, 2002.
50. J.C.S. Rebelo and R. Silva, The multiple ergodicity of non-discrete subgroups of Diff.
(S1), Moscow Mathematical Journal, 1-49, 2002.
51. N.M. Santos, Actions of Lie groups on closed manifolds, Ergodic Theory Dynamical
Systems, 22, 591-600, 2002.
52. N.M. Santos, M.S. Pereira, On the cohomology of foliated bundles, ProyeccionesRevista de Matemática, 21(2), 173-195, 2002.
53. P.A. Schweitzer, S.J. and J.L. Arraut, A note on actions of the cylinder S1 x R, Top.
Appls., 123, 533-535, 2002.
54. P.L.Q. Pergher, On (Z2)K Actions, Topology Appl, 117(1), 105-112, 2002.
55. P.L.Q.Pergher, (Z2)K Actions fixing {point} U Vn, Fundamenta Math.,172(1), 83-97,
2002.
56. R.O.R. Rodriguez, An introduction to the study of variational and topological aspects of
invariant tori of the geodesic flow of surfaces, Monografia, Instituto de Matemática y
Ciencias Afines, IMCA, Lima, Peru, 2002.
57. S. Druck, F. Fang and S. Firmo, Fixed points of discrete nilpotent groups actions on
S2, Ann. Inst. Fourier, 52-4, 1073-1089, 2002.
58. S. Druck, M. Boileau, E. Vogt, A vanishing theorem for the Gromov volume of 3manifolds with an application to circle foliations, Mathematische Annalen, 322(3), 493524, 2002.
Papers in Topology accepted for publication
1. Daciberg L. Gonçalves and Albrecht Dold, Self-coincidence of fibre maps, Osaka
Journal of Mathematics in June/30/2004.
2. Daciberg L. Gonçalves and Duane Randall, Self-coincidence of maps from Sq-bundles
over Sn to Sn, BSM, March 2004.
3. Daciberg L. Gonçalves and John Guaschi Braid groups of the Projective plane, ATG in
July/2004.
4. Daciberg L. Gonçalves and Peter Wong, Obstruction theory and coincidences of maps
between nilmanifolds, Archiv der Mathematik, 19/July/2004.
5. Daciberg L. Gonçalves and Peter Wong, Wecken properties for roots, in PAMS
05/01/2004.
6. Daciberg L. Gonçalves John Guaschi, The braid group Bm,n(S2) and a generalisation of
the Fadell-Neuwirth short exact sequence, Jktr 04/30/2004.
100
7. Daciberg L. Gonçalves, Jan Jaworowsky, Pedro Pergher and Alexei Volovikov,
Coincidences for maps of spaces with finite group actions, Top. and Its Applic. in
May/20/2004.
8. P.H.C. Gusmão, A. Sarmiento, Foliations on 3-manifolds which are the classifying
space of themselves, Boletim da SBM, 2004.
9. Rodriguez, R. O. R., Carneiro, M. J. D, On variational and topological properties of C1
invariant Lagrangian tori. Ergodic Theory and Dynamical systems. Cambridge,
Inglaterra, 2002. Ergodic Theory and Dynamical Systems, 2004.
10. Biasi, C., de Mattos, Denise, dos Santos, Edivaldo L. A Borsuk-Ulam Theorem for
Maps from a Sphere to a Generalized Manifolds, Geometriae Dedicata, 2003.
11. Daciberg L. Gonçalves and Arcadiy Skopenkov, Embeddings of highly-connected
manifolds with boundary, Math. Zametki, February 2003.
12. Daciberg L. Gonçalves and João Vieira Peres, Free action of abelian p-groups on the
n-torus, Houston Journal of Mathematics, July 2003.
13. Daciberg L. Gonçalves and John Guaschi, On the roots of the full twist, Accepted in
Proceedings of the Cambridge Philosophical Society, January/22/03).
14. Daciberg L. Gonçalves and Marek Golasinski, Spherical Space forms-Homotopy types
and self-equivalences for the groups Z/a x Z/b and Z/a x (Z/b x Q2i), Top and its
applications (Japan Conference), March-2003.
15. Daciberg L. Gonçalves and Peter Wong, Homogeneous spaces in coincidence theory
II, Forum, 1 July 2003.
16. Daciberg L. Gonçalves, Coincidence Theory, Handbook of Fixed-Point TheoryElsevier, September/2003.
17. Daciberg L. Gonçalves, Semeon Bogatyi, Heiner Zieschang and Elena Kudryavtseva,
Realization of primitive branched coverings of surfaces, Kluwer, Calgary Conference,
August 2003.
18. M.A. Bertolim, M.P. Mello and K.A. de Rezende, Dynamical and Topological Aspects
of Lyapunov Graphs, Qualitative Theory of Dynamical Systems, 2003.
19. M.A. Bertolim, M.P. Mello and K.A. de Rezende, Lyapunov Graphs, Poincaré-Hopf
and Morse Inequalities, Ergodic Theory and Dynamical Systems, 2003.
20. M.A. Bertolim, M.P. Mello and K.A. de Rezende, Poincaré - Hopf Inequalities, Trans.
of the Amer. Math. Soc., 2003.
Preprints
1. Fernando Alcalde Cuesta, Gilbert Hector e Paul A. Schweitzer, S.J., A generalization
of Novikov's Theorem on the existence of Reeb components in codimension one
foliations, preprint, 2004
2. Rebelo, J. C. S., A. L. Silva, On the Burnside problem in Diff(M), Submetido a
Geometry and Topology, 2004.
3. S. Firmo, A note on commuting diffeomorphisms on surfaces, preprint, 2004.
4. S. Firmo, Fixed points of discrete nilpotent group actions on surfaces, preprint, 2004.
5. Alexandrino, M. M., Folheações riemannianas singulares com seções, 2003.
101
6. Alexandrino, M. M., Folheações riemannianas singulares com seções e aplicações
transnormais, 2003.
7. Alexandrino, M. M., Singular riemannian foliations with sections, 2003.
8. Alexandrino, M. M., Singular riemannian foliations with sections. Preprints. Arxiv.org,
2003. http://arxiv.org/PS_cache/math/pdf/0311/0311454.pdf
9. M.A. Bertolim, G.M. Vago and K.A. de Rezende, Minimal Morse Functions on
Compact Manifolds, Submetido ao Topology and its Applications.
10. Rebelo, J. C. S., The structure of the singularities of holomorphic flows in dimension 3,
I. Preprint, 2003.
Singularities of Differentiable Maps
Research articles accepted for publication
1. Aroca, F. and Snoussi, J., Normal Quasi-ordinary singularities, Seminaires et Congrès,
Société Mathematique de France, 2004.
2. Aroca, F., Puiseux parametric equations of analytic sets, Proc. of the AMS, 132: 30353045, 2004.
3. D. Levcovitz, V.H. Jorge Perez, M.J. Saia, Invariants, equisingularity and Euler
obstructions of map-germs from C n to C n, J. für die reine und ang. Math., 2004.
4. Fernandes, A. C. G., Soares Jr, C. H., Bilipschitz triviality in families of real maps,
Proceedings of the VIII Workshop. Contemp. Math. AMS. Providence, RI. 354, 2004.
5. Fernandes, A.C.G. and Ruas, M.A.S., Bilipschitz determinacy of quasihomogeneous
germs, Glasgow Math. J., 46, 77-82, 2004.
6. Fernandes, Alexandre C. G., Gutierrez, C., Rabanal, R., Global asymptotic stability for
differentiable vector fields of R 2, Journal of Differential Equations, 2004.
7. Furter, J., Ruas, M.A.S. and Sitta, A., Singularity theory and forced symmetry breaking
in equations, Nonlinear Analysis, Theory, Methods and Applications, 2004.
8. Furter, J.E. and Sitta, A.M., A note on non-degenerate umbilics and the path
formulation for bifurcation problems, Proc. Royal Soc. of Edinburgh, 2004.
9. Furter, J.E. and Sitta, A.M., A note on the path formulation for O(2)/SO(2) symmetry
breaking bifurcation, Real and Complex Singularities, Contemporary Mathematics,
354, AMS, 2004.
10. Furter, J.E. and Sitta, A.M., Path formulation for equivariant bifurcation problems: the
D3 classification, Math. Proc. Camb. Ph. Soc., 2004.
11. L. Birbrair and F.Cano, Characteristic exponents of semialgebraic singularities,
Mathematische Nachrischten, 2004.
12. Labouriau, I. and Ruas, M.A.S., Invariants for bifurcations, Houston Math. J., 2004.
13. Mancini, S., Manoel, M., and Teixeira, M.A., Divergent diagrams of folds and
simultaneous conjugacy of involutions, Discrete and Continous Dynamical Systems,
2004.
14. Oliveira, R.D.S., Families of pairs of Hamiltonian vector fields in the plane,
Proceedings of the VII Workshop on Real and Complex Singularities, Contemporary
Mathematics, 354, 2004.
102
15. Rieger, J. and Ruas, M.A.S., M-deformations of A-simple Sigma n-p+1-germs from Rn
to R p, n = p, Math. Proc.Cambridge Phil. Soc., September 2005, 2004.
16. Ruas, M.A.S. and Tomazella, J., Topological triviality of families of sections of analytic
varieties, Nagoya Math. Journal, September 2004.
17. Saia, M. J. and Tomazella, J.N., Deformations with constant Milnor number and
multiplicity of complex hypersurfaces, Glasg. Math. J., 46(1), 121-130, 2004.
18. Saia, M. J. and Zuniga-Galindo, W.A., Local zeta function for curves non-degeneracy
conditions and Newton polygons, Transactions A.M.S., 2004.
19. Santos, R. N., Topological Triviality of Families of Real Isolated Singularities and their
Milnor Fibrations, Mathematica Scandinavica, 2004.
20. Birbrair, L., Sobolevsky, M. and Sobolevskii, P., Focal decompositions for linear
differential equations of the second order, in Abstract and Applied Analysis, 14, 813821, 2003.
21. D. Hacon, C. Mendes de Jesus y M.C. Romero Fuster, Global topological invariants of
stable maps from a surface to the plane. Lecture Notes in Pure and Applied Maths,
232, Marcel Dekker, 2003.
22. D. Mond and M. J.Saia, Lecture Notes in Pure and Applied Math. 232, Marcel Dekker,
283-300, 2003.
23. Fernandes, Alexandre C.G., Topological equivalence of complex curves and biLipschitz maps. Michigan Mathematical Journal, 51(3), 593-606, 2003.
24. Gutierrez, C. and Ruas, M.A.S., Indices of Newton non-degenerate vector fields and a
conjecture of Loewner for surfaces in R4, Real and Complex Singularities, ed. by D.
Mond and M. J.Saia, Lecture Notes in Pure and Applied Mathematics 232, Marcel
Dekker, 2003, 245-253.
25. Jorge Perez, V.H., Multiplicities and equisingularity of map germs from C3 to C3
Houston Journal of Mathematics, 29(4), 901-924, 2003.
26. Jorge Perez, V.H., Polar Multiplicity and Equisingularity of map Germ from C3 to C4.
Proceedings of the VI Workshop at São Carlos, Lecture Notes in Pure and Applied
Maths, 207-226, 2003.
27. Marar, W.L., Superfícies singulares, Revista Matemática Universitária da SBM, 33,
2003.
28. Mochida, D. H., Romero-Fuster, M. C. and Ruas, M. A. S.; Inflection points and nonsingular embeddings of surfaces in R 5. Rocky Mountain Journal of Math., 33(3), 2003.
29. Mond, D. and Wik Atique, R.; Not all codimension 1 germs have good real pictures,
Real and Complex Singularities, ed. D. Mond and M. J.Saia, Lecture Notes in Pure
and Applied Math. 232, Marcel Dekker, 189-200, 2003.
30. Nabarro, A.C., Duality and contact of hypersurfaces in R4 with hyperplanes an lines,
Proc. Edinburgh Math. Soc. 46, 637-648, 2003.
31. Nabarro, A.C., Projections of hypersurface in R4 to planes; Real and Complex
Singularities, ed.
32. S.M. Moares, M.C. Romero-Fuster, F. Sanchez-Bringas, Principal configurations and
umbilicity of submanifolds in R n, Bulletin of the Belgian Mathematical Society, 2003.
103
33. S.M. Moares, M.C. Romero-Fuster, Semiumbilics and Normal Fields on Surfaces
Immersed in R n, n>3, Rocky Mountain Journal of Math., 2003.
34. Birbrair, L. and Brasselet, J-P., Metric Homology for isolated conical singularities, Bull.
Sci. Math., 126, 87-95, 2002.
35. Bruce, J.W. and Tari, F., Families of surfaces in R4, Proc. Edinburgh Math. Soc.,
45(2), 181-203, 2002.
36. Cooper, T., Mond, D. and Wik Atique, R., Vanishing topology of codimension 1 multigerms over R and C. Compositio Math., 131, 121-160, 2002.
37. Fukui, T., Bivia-Ausina, C. and Saia, M.J., Newton filtrations, Graded algebras and
codimension of ideals, Math. Proc. of the Cambridge Phil.Soc., 133(1), 55-75, 2002.
38. Furter, J.E. and Sitta, A.M., Dn-forced symmetry breaking of O(2)-equivariant
bifurcation problem, Proc. Royal Soc. of Edinburgh, 132A, 1185-1218, 2002.
39. Jorge Perez, V.H., Weighted homogeneous map germs from C3 to C3 and polar
multiplicity, Proyecciones 21(3), 245-259, 2002.
40. Mancini, S. and Ruas, M.A.S. and Teixeira, M.A., On divergent diagrams of finite
codimension, Portugaliae Math., 59(2), 2002.
41. Oliveira, R.D.S. and Tari, F., On pairs of regular foliations in the plane, Hokkaido
Mathematical Journal, 6(3), 523-537, 2002.
42. Ruas, M.A.S., Seade, J. and Verjovsky, A., On real singularities with a Milnor fibration,
Trends in singularities, 191-213, Trends Math., Birkhäuser, Basel, 2002.
Books published in Singularity Theory
1. Real and Complex Singularities, Contemporary Mathematics, 354, AMS, 2004, Edited
by Terence Gaffney, Northeastern University, Boston, MA and Maria Aparecida
Soares Ruas, ICMC-USP, São Carlos, S.P., Brasil.
2. Real and Complex Singularities, Marcell-Decker, Lecture Notes in Pure and Applied
Maths., Marcell Decker Inc-New York. Edited by Marcelo Jose Saia, ICMC-USP, São
Carlos, S.P., Brasil, and David Mond, University of Warwick, U.K.
Doctoral Degrees in Topology and Singularity Theory 2002-2004
1. Ana Lucia da Silva. Sobre o problema de Burnside em Diff (M). ICMC-USP, 2004.
Advisor: Julio Cesar de Souza Rebelo
2. José Barbosa Gomes Rigidez de superfícies cujos fluxos geodésicos preservam
folheações de codimensão um PUC-Rio, 29 January 2004. Advisor: Rafael Oswaldo
Ruggiero Rodríguez
3. Marcelo Buosi. Imersões horojustas em espaços hiperbólicos, ICMC-USP, defense
planned for September 2004. Advisor: Maria Aparecida Soares Ruas
4. Carlos Humberto Soares Junior. Poliedros de Newton e trivialidade em famílias de
aplicações. ICMC-USP, May 2003. Advisor: Marcelo José Saia
5. Jose Carlos de Sousa Junior. Aneis d-simples e ideais maximais da algebra de Weyl,
ICMC-USP, February 2003. Advisor: Daniel Levcovitz
104
6. Liane Mendonça Feitosa . Trivialidade topológica de germes pre quase homogêneos.
ICMC-USP, August 2003. Advisor: Marcelo José Saia
7. Luciana de Fátima Martins Brito. Folheações Singulares em D2 x S1. ICMC-USP,
2003. Advisor: José Luis Arraut Vergara
8. Luís Fernando Crocco Afonso, Representações de grupos triangulares em geometria
hiperbólica complexa, PUC-Rio, 29 August 2003. Advisor: Nikolai Goussevskii and
Paul A. Schweitzer.
9. Seme Gebara Neto, Domínios fundamentais de Ford para grupos discretos de
isometrias hiperbólicas complexas, UFMG, 11 December 2003. Advisor: Nikolai
Goussevskii.
10. Alexandre Cesar Gurgel Fernandes. Teoria métrica de curvas complexas. ICMC-USP,
27 March 2002. Advisor: Maria Aparecida Soares Ruas
11. Carlos Alberto Maquera Apaza. Ações de Rn em Mm com 2 ≤ n ≤ m ≤ 3. ICMC-USP,
2002. Advisor: José Luis Arraut Vergara
12. Claudemir Aniz. Índice de Classes de Coincidências em Superfícies; ICMC-USP, 12
September 2002. Advisor: Daciberg Lima Gonçalves.
13. Daniel Vendrúsculo. Teoria de coincidência equivariante e números de Nielsen
equivariante, IME-USP, 25 April 2002. Advisor: Daciberg Lima Gonçalves.
14. Francisco Dutenhefner, Representacões de Grupos Fuchsianos no Espaço
Hiperbolico Complexo, UFMG, 21 June 2002. Advisor: Nikolai Goussevskii.
15. Leonardo Navarro de Carvalho, Automorfismos genéricos de cubos com alças, PUCRio, 01 November 2002. Advisor: Paul A. Schweitzer and Ulrich Oertel.
16. Magno Branco Alves. Sobre redução de singularidades de fluxos holomorfos em
dimensão três, PUC-Rio, 25 March 2002. Advisor: Julio Cesar Rebelo.
17. Marcos Martins Alexandrino da Silva, Folheações riemannianas singulares com
seções e aplicações transnormais, PUC-Rio, 23 September 2002. Advisor: Ricardo Sá
Earp aand Gudlaugur Thorbergsson.
18. Maria Alice Bertolim. Grafos de Lyapunov, desigualdades de Poincaré-Hopf e de
Morse, ICMC-USP, 2002. Advisor: Ketty Rezende e Ozíride Manzoli Neto.
19. Raimundo Nonato Araujo dos Santos. Fibrações de Milnor Reais. ICMC-USP, 25
May 2002. Advisor: Maria Aparecida Soares Ruas
20. Rogério de Oliveira, Involuções comutante fixando dois espaços projetivos pares,
UFSCar, 2002. Advisor: Pedro Luiz Pergher.
21. Simone Maria de Moraes. Elipses de curvatura em superfícies imersas no Rn.
IMECC-UNICAMP, February 2002. Advisor: Sueli Irene Rodrigues Costa and Maria
del Carmen Romero Fuster
105
Combinatorics and Algorithms
The contribution of IM-AGIMB in the development of combinatorics in the country
The Millenium Institute IM-AGIMB has strongly promoted the scientific activities in
combinatorics and algorithms in the country. Broadly speaking, its support has generally
been in the form of promoting specialized scientific meetings and in the form of promoting
visits of renowned researchers to the country. For example, IM-AGIMB was instrumental
in bringing to Brazil researchers such as N. Alon (Tel Aviv), B. Bollobás (Memphis and
Cambridge), P. Pudlák (Czech Acad. Sciences), B. Reed (McGill), and V. Rödl (Emory
Univ.), all speakers of the International Congress of Mathematicians, and G. Cornuéjols
(Carnegie Mellon) and A. Frieze (Carnegie Mellon), both winners of the Fulkerson Prize.
Despite the fact that the area of combinatorics and algorithms has strong roots in the
country and the fact that the research carried out in Brazil is internationally recognized, the
area still needs to grow considerably. This subject usually involves researchers working in
mathematics departments and computer science departments. IM-AGIMB has induced a
stronger interaction among researchers and students from diverse departments, subareas,
and with a varied range of interests, thus strengthening combinatorics as a whole in the
country.
It is also worth mentioning that combinatorics and algorithms may have a special role to
play in several interdisciplinary areas, for being a natural bridge subject connecting
mathematics and certain areas of modern science. IM-AGIMB has the potential of
establishing and promoting such interdisciplinary activities.
In any form of support, the agile and flexible structure of IM-AGIMB has been a decisive
feature for the success of the proposed research or scientific activity.
The impact of IM-AGIMB on the organization of scientific meetings and on the
organization of visits of national and international researchers
IM-AGIMB has played a prominent role in the promotion of, among others, the following
meetings in the area of combinatorics and algorithms in the country:
•
Workshop on Combinatorics, Probability, and Computing, 12-14/February 2004, IMPA,
Rio de Janeiro, RJ.
•
Workshop on Combinatorics, Random Structures, and Algorithms, 12-13/March 2003,
IMPA, Rio de Janeiro, RJ.
•
Workshop on Combinatorics, Algorithms, and Applications, 1-5/September 2003,
Ubatuba, SP.
•
Extended Workshop on Combinatorics, 4-14/March 2002, São Paulo/Ubatuba/Rio de
Janeiro.
Among the participants of these meetings, we mention the following researchers, all of
them of international renown:
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Alan Frieze (Carnegie Mellon), Alfredo Viola (U. de la Republica), Andrew Thomason
(Cambridge), Béla Bollobás (Memphis e Cambridge), Brendan Nagle (Georgia Tech.),
Bruce Reed (McGill), Bruce Richmond (Waterloo), Christian Mauduit (Luminy), Dwight
Duffus (Emory University), Esko Ukkonen (U. of Helsinki), Gérard P. Cornuéjols (Carnegie
Mellon), Hanno Lefmann (T.U. Chemnitz), Jeremy Spinrad (Vanderbilt), Jozef Skokan
(Urbana-Champaign) Louis H. Kauffman (Chicago), Marcos Kiwi (U. de Chile), MarieFrance Sagot (INRIA, Rhône-Alpes), Oliver Riordan (Cambridge), Pavel Pudlák
(Academia Tcheca de Ciências), Prabhakar Raghavan (Verity and Stanford), U.S.R. Murty
(Waterloo), Vojtech Rödl (Emory University).
It should be pointed out that, among the above researchers, we have speakers of the
Internation Congress of Mathematicians (Bollobás, Pudlák, Reed, and Rödl) and winners
of the Fulkerson Prize (Cornuéjols and Frieze).
Finally, we mention that in the Brazilian Mathematics Colloquium in 2003, another meeting
that was promoted by IM-AGIMB, and one of the plenary speakers was Noga Alon (Tel
Aviv Univ.), an eminent, leading figure in combinatorics.
Advances in the area in the past 30 months in the country
Substantial part of the advances in the area of combinatorics and combinatorial algorithms
in the country, in the past 30 months, naturally fall into some subareas:
(1) Graph theory. Carvalho, Lucchesi, and Murty succeeded to further their investigation
of the structure of matchings in graphs covered by perfect matchings. This work is in part
inspired on some classical work of Lovász. Substantial part of the results of those authors
was published in a series of three papers in the J. Combinatorial Theory B, one of the
most prestigious journals in the area, in 2002. Also in the area of graph theory, de
Figueiredo and her collaborators and Szwarcfiter and his collaborators were very
successful in several fronts, as their publications in the period show.
(2) Matroid theory. Lemos and Oxley obtained several structural and extremal results for
matroids and graphs. Two important papers on the subject are due to Lemos and to
Lemos and Oxley: the first considers some previous work of Cunningham and Seymour on
the reconstructibility of binary matroids, up to duality, from their connectivity functions, and
the second considers some work due to Mader, on the existence of removable cycles in 2connected graphs. These two papers were published in the J. Combinatorial Theory B
and in the J. Graph Theory.
(3) Pseudorandomness and random graphs. Kohayakawa and Rödl and their coauthors continued their work on pseudorandom graphs and hypergraphs, on the regularity
lemma of Szemerédi and its variants, and on random graphs. Their results were published
in journals such as Combinatorics, Probability, and Computing, Israel J. Mathematics, J.
Combinatorial Theory A, Random Structures and Algorithms, and SIAM J. Computing.
(4) Combinatorial algorithms. The investigation of the design and analysis of
combinatorial algorithms had several facets. The focus of this research ranged from graph
algorithms to high dimensional, geometric packing algorithms. The results in this area
were published in Algorithmica, J. Algorithms, SIAM J. Computing, Information Proc.
Letters, and Theoret. Comput. Sci.
107
(5) Applications. In the country, bioinformatics was the applied line of research within
combinatorics, algorithms, and computing that had the strongest impact. In this area,
several papers were published in journals such as Nature, Nature Genetics, Annual
Review of Phytopathology, Yeast, and J. Bacteriology.
Springer-Verlag published a book containing several surveys on combinatorial topics on
which there are well known specialists in the country. This book, published in 2003,
includes chapters on (a) matching covered graphs (Carvalho, Lucchesi, and Murty), (b)
pseudorandomness and the regularity lemma (Kohayakawa and Rödl), (c) sequence
analysis in computational biology (Sagot and Wakabayashi), and (d) clique graphs
(Szwarcfiter).
Journal publications 2002-2004
1. C.G. Fernandes, E.L. Green and A. Mandel, From monomials to words to graphs. J.
Combin. Theory Ser. A , 105(2), 185-206, 2004.
2. C.G. Moreira and Y. Kohayakawa, Bounds for optimal coverings. Discrete Appl. Math.,
141(1-3), 263-276, 2004.
3. G.D. da Fonseca, C.M.H. de Figueiredo, and P. C. P. Carvalho, Kinetic hanger,
Information Processing Letters, 89, 151-157, 2004.
4. L. Faria, C.M.H. de Figueiredo, and C.F.X. de Mendonça Neto, On the complexity of
the approximation of nonplanarity parameters for cubic graphs, Discrete Applied
Mathematics, 141, 119-134, 2004.
5. M. Lemos and J. Oxley, On the minor-minimal 2-connected graphs having a fixed
minor. Discrete Math., 280(1-3), 77-118, 2004.
6. M. Lemos, Non-separating cocircuits in binary matroids. Linear Algebra Appl., 382,
171-178, 2004.
7. R. Carmo, J. Donadelli, Y. Kohayakawa, E. Laber, Searching in random partially
ordered sets. Theoret. Comput. Sci. 321(1), 41-57, 2004.
8. Y. Kohayakawa, F.K. Miyazawa, P. Raghavan, and Y.
Multidimensional cube packing, Algorithmica, 40(3), 173-187, 2004.
Wakabayashi,
9. Y. Kohayakawa, V. Rödl, and M. Schacht, The Turán theorem for random graphs,
Combinatorics, Probability, and Computing, 13(1), 61-91, 2004.
10. Y. Kohayakawa, V. Rödl, and P. Sissokho, Embedding graphs with bounded degree in
sparse pseudorandom graphs. Israel J. Math., 139, 93-137, 2004.
11. Bondy and G. Durán, M.C. Lin, and J.L. Szwarcfiter, Self-clique graphs and matrix
permutations. J. Graph Theory, 44(3), 178-192, 2003.
12. C.M.H. de Figueiredo and G.D. Fonseca, Kinetic heap-ordered trees: tight analysis and
improved algorithms, Information Processing Letters, 85, 165-169, 2003.
13. C.M.H. de Figueiredo, J. Meidanis, C.P. de Mello, and C. Ortiz, Decompositions for the
edge colouring of reduced indifference graphs, Theoretical Computer Science, 297,
145-155, 2003.
14. C.P. de Mello and A. Morgana, The clique operator on extended P4-sparse graphs,
Matematica Contemporanea 25, 33-47, 2003.
108
15. D. Ferber, T. Dias, A. Moura, and C.C. de Souza, Constructing Nurse Schedules at
Large Hospitals, International Transactions in Operations Research, 10, 245-265,
2003.
16. E. Friedgut, Y. Kohayakawa, V. Rödl, A. Rucinski, and P. Tetali, Ramsey games
against a one-armed bandit, Combinatorics, Probability, and Computing, 12, 515-545,
2003.
17. F. Calheiros, A. Lucena, and C.C. de Souza, Optimal Rectangular Partition,
Networks, 41(1), 51-67, 2003.
18. F.K. Miyazawa and Y. Wakabayashi, Cube packing, Theoretical Computer Science,
297(1-3), 355-366, 2003.
19. F.K. Miyazawa and Y. Wakabayashi. Parametric on-line approximation algorithms for
packing rectangles and boxes, European Journal of Operational Research, 150, 281292, 2003.
20. G. Calinescu, C.G. Fernandes, and B. Reed, Multicuts in Unweighted Graphs and
Digraphs with Bounded Degree and Bounded Tree-Width, Journal of Algorithms, 48
(2), 333-359, 2003.
21. G. Calinescu, C.G. Fernandes, H. Karloff, and A. Zelikovski, A new
approximation
algorithm for finding heavy planar subgraphs, Algorithmica, 36, 179-205, 2003.
22. J.C. de Pina and J. Soares, Improved bound for the Carathodory rank of the bases of a
matroid, Journal of Combinatorial Theory (B), 88(2), 323-327, 2003.
23. J.L. Szwarcfiter, G. Navarro, R. Baeza-Yates, J. de S. Oliveira, W. Cunto, N. Ziviani,
Optimal binary search trees with costs depending on the access paths. Theoret.
Comput. Sci., 290(3), 1799-1814, 2003.
24. M. Gutierrez and J. Meidanis, Recognizing Clique Graphs of Directed Edge Path
Graphs, Discrete Applied Mathematics, 126(2-3), 297-304, 2003.
25. M. Lemos and J. Oxley, On removable cycles throught every edge, Journal of Graph
Theory, 42, 155-164, 2003.
26. M. Lemos and J.G. Oxley, On the minor-minimal 3-connected matroids having a fixed
minor, European Journal of Combinatorics, 24, 1097-1123, 2003.
27. M. Lemos, Matroids with many common bases, Discrete Mathematics, 270, 192-204,
2003.
28. M. Lemos, Uniqueness of the decomposition of the rank function of a 2-polymatroid,
Discrete Mathematics, 269, 161-179, 2003.
29. M.C. Dourado, F. Protti, and J.L. Szwarcfiter, The (p,q)-Helly property
and its
application to the family of cliques of a graph. The Latin-American Workshop on
Cliques in Graphs (Rio de Janeiro, 2002). Mat. Contemp., 25, 81-90, 2003.
30. N.C. Saldanha and C. Tomei, Tilings of quadriculated annuli. J. Combin. Theory Ser.B,
88(1), 153-183, 2003.
31. N.F. Almeida Jr., J.C. Setubal, M.A. Van Sluys, et al. Comparative analyses of the
complete genome sequences of Pierce's Disease and Citrus Variegated Chlorosis
strains of Xylella fastidiosa, Journal of Bacteriology, 185(3), 1018-1026, 2003.
109
32. N.F. Almeida Jr., M.S.S. Felipe, et al. Transcriptome characterization of the dimorphic
and pathogenic fungus Paracoccidioides brasiliensis by EST analysis, Yeast 20, 3,
263-271, 2003.
33. O. Alves, C.E. Ferreira, and F.P. Machado, Estimates for the Spreading Velocity of an
Epidemic Model, Mathematics and Computers in Simulation, 64-66, 609-616, 2003.
34. R.L. Milidiú, A.A. Pessoa, E.S. Laber, The complexity of makespan minimization for
pipeline transportation. Theoret. Comput. Sci. 306(1-3), 339-351, 2003.
35. S. Verjovski-Almeida, E. Dias-Neto, L.C. Leite, J.C. Setubal, J.P. Kitajima, and J.P.
Piazza, Transcriptome analysis of the acoelomate human parasite Schistosoma
mansoni. Nature Genetics, 35, 1-10, 2003.
36. T. Feder, P. Hell, S. Klein, and R. Motwani, List Partitions. SIAM Journal on Discrete
Mathematics, 16(3), 449-478, 2003.
37. V. Dias, G. Fonseca, C.M.H. de Figueiredo, and J. Szwarcfiter, The stable marriage
problem with restricted pairs, Theoretical Computer Science, 306, 391-405, 2003.
38. Y. Kohayakawa and V. Rödl, Regular pairs in random graphs I, Random Structures
and Algorithms, 22 (4), 359-434, 2003.
39. Y. Kohayakawa and V. Rödl, Regular pairs in sparse random graphs I. Random
Structures Algorithms, 22(4), 359-434, 2003.
40. Y. Kohayakawa, B. Nagle, and V. Rödl, Hereditary properties of triple systems,
Combinatorics, Probability, and Computing, 12(2), 55-189, 2003.
41. Y. Kohayakawa, V. Rödl, and L. Thoma, An optimal algorithm for checking regularity,
SIAM Journal on Computing, 32(5), 1210-1235, 2003.
42. C.E. Ferreira, C.C. de Souza, and Y. Wakabayashi, Rearrangement of DNA
fragments: a branch-and-cut algorithm, Discrete Applied Mathematics, 116 (1-2), 161177, 2002.
43. C.M.H. de Figueiredo, J. Gimbel, C.P. de Mello, and J. L. Szwarcfiter. A note on
transitive orientations with maximum sets of sources and sinks. Discrete Applied
Mathematics, 120(1-3), 91-95, 2002.
44. C.M.H. de Figueiredo, S. Klein, and K. Vuskovic, The graph sandwich problem for 1join composition is NP-complete, Discrete Applied Mathematics, 121(1-3), 73-82, 2002.
45. E.S. Laber, L.G. Holanda, Improved bounds for asymmetric communication
protocols. Inform. Process. Lett., 83(4), 205-209, 2002.
46. E.S. Laber, R.L. Milidiú, A.A. Pessoa, A strategy for searching with different access
costs. Algorithms (Prague, 1999). Theoret. Comput. Sci., 287(2), 571-584, 2002.
47. E.S. Laber, R.L. Milidiú, A.A. Pessoa, On binary searching with nonuniform costs.
SIAM J. Comput., 31(4), 1022-1047, 2002.
48. F. Protti, J.L. Szwarcfiter, Clique-inverse graphs of bipartite graphs. J. Combin. Math.
Combin. Comput., 40, 193-203, 2002.
49. G. Durán, M.C. Lin, and J.L. Szwarcfiter, On clique-transversals and cliqueindependent sets. Operations research and systems (CLAIO 2000), Part I (Mexico
City). Ann. Oper. Res., 116, 71-77, 2002.
110
50. H. van der Holst and J.C. de Pina, Length-bounded disjoint paths in planar graphs.
Sixth Twente Workshop on Graphs 1nd Combinatorial Optimization (Enschede, 1999).
Discrete Applied Mathematics, 120(1-3), 251-261, 2002.
51. J. Donadelli and Y. Kohayakawa, A density result for random sparse oriented graphs
and its relation to a conjecture of Woodall, Electronic Journal of Combinatorics, 9(1),
Research paper 45, 10pp.
52. J. Meidanis, M.D.V. Braga, and S. Verjovski-Almeida, Whole-genome analysis of
transporters in the plant pathogen Xylella fastidiosa. Microbiology and Molecular
Biology Reviews, 66(2), 272-299, 2002.
53. J. Meidanis, M.M.T. Walter, and Z. Dias. A Lower Bound on the Reversal and
Transposition Diameter. Journal of Computational Biology, 9(5), 743-745, 2002.
54. L. Faria, C. M. H. de Figueiredo, J. Stolfi, C.F.X. de Mendona Neto, and E. F. Xavier.
The splitting number and skewness of C n x Cm. Ars Combinatoria, 63, 193-205, 2002.
55. L. Lins, S. Lins, and R. Morabito, An n-tet graph approach for non-guillotine packings of
n-dimensional boxes into an n-container, European Journal of Operational Research,
141(2), 421-439, 2002.
56. M. Gutierrez and J. Meidanis. On Clique Graph Recognition. Ars Combinatoria, 63,
207-210, 2002.
57. M. Gutierrez and J. Meidanis. Recognizing Clique Graphs of Directed Edge Path
Graphs. Discrete Applied Mathematics, 126, 297-304, 2002.
58. M. Lemos, On the connectivity function of a binary matroid, Journal of Combinatorial
Theory B, 86(1), 114-132, 2002.
59. M.A. van Sluys, C.B. Monteiro-Vitorello, L.E.A. Camargo, C.F.M. Menck, A.C.R. da
Silva, J.A. Ferro, M.C. Oliveira, 2 RC. Setubal, J.P. Kitajima, and A.J.G. Simpson.
Comparative genomic analysis of plant-associated bacteria. Annual Review of
Phytopathology, 40, 169-189, 2002.
60. M.H. Carvalho, C.L. Lucchesi, and U.S.R. Murty, Optimal ear decompositions of
matching covered graphs and bases for the matching lattice, Journal of
Combinatorial Theory B, 85(1), 59-93, 2002.
61. M.H. Carvalho, C.L. Lucchesi, and U.S.R. Murty. On a conjecture of Lovász
concerning bricks I: The characteristic of a matching covered graph. Journal of
Combinatorial Theory (B), 85(1), 94-136, 2002.
62. M.H. Carvalho, C.L. Lucchesi, and U.S.R. Murty. On a conjecture of Lovász
concerning bricks II: Bricks of finite characteristic. Journal of Combinatorial Theory B,
85(1), 137-180, 2002.
63. M.R. Cerioli and J.L. Szwarcfiter, Edge clique graphs and some classes of chordal
graphs, Discrete Mathematics 242, 31-39, 2002.
64. N.C. Saldanha, Singular polynomials of generalized Kasteleyn matrices. J. Algebraic
Combin., 16(2), 195-207, 2002.
65. N.F. Almeida Jr., J.C. Setubal, J. Meidanis, et al., Comparison of the genomes of two
Xanthomonas pathogens with differing host specificities. Nature, 417, 459-463, 2002.
66. O. Lee and Y. Wakabayashi, On the circuit cover problem for mixed graphs.
Combinatorics, Probability and Computing, 11, 43-59, 2002.
111
67. S. Kingan and M. Lemos, Almost graphic matroids, Advances in Applied
Mathematics 28(3-4), 438-477, 2002.
68. S. Lins and M. Mulazzani, Isomorphisms and homeomorphisms of a class of graphs
and spaces. Aequationes Mathematicae, 64(1-2), 110-127, 2002.
69. Y. Kohayakawa, V. Rödl, and J. Skokan, Hypergraphs, quasi-randomness, and
conditions for regularity, Journal of Combinatorial Theory A, 97(2), 307-352, 2002.
Ph.Ds. 2002-2004
1. Glauber Ferreira Cintra.
Algoritmos para problemas de corte de guilhotina
bidimensional. Advisor: Yoshiko Wakabayashi (IME-USP), 2004.
2. Liliane Rose Benning Salgado. Algoritmos de aproximação para partições conexas
em grafos. Advisor: Yoshiko Wakabayashi (IME-USP), 2004.
3. Artur Alves Pessoa. Dois problemas de otimização em grafos: transporte em redes de
dutos e busca com custos de acesso. Advisor: Ruy Luiz Milidiú (DI-PUC-RJ), 2003.
4. Elder Magalhes Macambira. Uma abordagem poliédrica para problemas de otimização
combinatória com aplicações no planejamento de redes telefônicas. Advisors: N.
Maculan (COPPE-UFRJ) and C.C. de Souza (IC-UNICAMP), 2003.
5. Emerson Alexandre de Oliveira Lima. Códigos de Gauss não 2-face coloríveis em
RP2. Advisor: Sóstenes Lins (DM-UFPE), 2003.
6. Estela Maris Rodrigues. Algoritmos para construção de árvores filogenéticas e o
problema dos pontos de recombinaço. Advisor: Yoshiko Wakabayashi, 2003.
7. Loana Tito Nogueira. Particionamento e extensão de grafos cordais em conjuntos
independentes e cliques. Advisor: S. Klein (IM-COPPE-UFRJ), 2003.
8. Marco Aurélio Stefanes. Algoritmos paralelos de granularidade grossa em grafos
bipartidos convexos. Advisor: J.A.R. Soares (IME-USP), 2003.
9. Pablo Coll. A polyhedral approach to scheduling unrelated processors under.
Advisors: C.C. Ribeiro/DI-PUC-Rio and C.C. de Souza (IC-UNICAMP), 2003.
10. Guilherme Pimentel Telles. Um algoritmo quase-linear para árvores PQR e um
esquema para clustering de seqüências expressas de cana-de-açúcar. Supervisor: J.
Meidanis (IC-UNICAMP), 2002.
11. Jair Donadelli Júnior. Resultados de Ramsey e de densidade para grafos pseudoaleatórios esparsos. Supervisor: Y. Kohayakawa (IME-USP), 2002.
12. Nalvo Franco de Almeida Jr.
Ferramentas computacionais para genômica.
Supervisor: J.C. Setubal (IC-UNICAMP), 2002.
13. Simone Dantas de Souza. Partições em grafos: caracterizações, algoritmos e
complexidade. Supervisor: C.M.H de Figueiredo (IM-COPPE-UFRJ), 2002.
14. Zanoni Dias. Rearranjo de genomas: uma coletanea de artigos.
Meidanis (IC-UNICAMP), 2002.
112
Supervisor: J.
Operator Algebras/Harmonic Analysis
The conceptual advances took place in two different fronts. We obtained important
applications of our methods to study equivalence relations in the context of Bratteli
diagrams. Given such a diagram one considers the space of all paths, which gives a
compact topological space. The equivalence relation usually known as "tail-equivalence",
namely the relation according to which two paths agree after a finite number of steps is a
fundamental example. Our important achievement was to obtain an extremely satisfactory
description for the algebra associated to this relation, which we proved to be isomorphic to
the AF-algebra defined by Bratteli in terms of the given diagram. This characterization is
important since AF-algebras are fundamental examples of C*-algebras and they occur in
the study of phenomena such as the quantum Ising model.
In the second front we continued with the development of the techniques suggested by the
analytic line of research, which includes the above advances, in a purely algebraic context.
We were able to obtain the construction of the covariance algebra for a partial dynamical
system twisted by a very general cocycle. This area is so far only on its infancy but it is
already attracting the attention of several algebraists in Brazil and abroad, including Misha
Dokuchaev, Miguel Ferrero, Francisco César Polcino Milies, Antonio Paques, Nadia
Zhukavets and B. Novikov, among others.
List of publications
1. R. Exel, KMS states for generalized gauge actions on Cuntz-Krieger algebras (An
application of the Ruelle-Perron-Frobenius Theorem), Bol. Soc. Brasil. Mat. (N.S.),
2004, [arXiv:math.OA/0110183].
2. S. Armstrong, K. Dykema, R. Exel, and H. Li, On embeddings of full amalgamated free
product C*-algebras, Proc. Amer. Math. Soc., 2004, [arXiv:math.OA/0210448].
3. R. Exel, A new look at the crossed-product of a C*-algebra by an endomorphism,
Ergodic Theory Dynam. Systems, 2004, [arXiv:math.OA/0012084].
4. M. Dokuchaev and R. Exel, Associativity of crossed products by partial actions,
enveloping actions and partial representations, Trans. Amer. Math. Soc., 2004,
[arXiv:math.RA/0212056].
5. Crossed-products by finite index endomorphisms and KMS states, J. Funct. Analysis,
199, 153-188, 2003, [arXiv:math.OA/0105195].
6. R. Exel and M. Laca, Partial dynamical systems and the KMS condition, Commun.
Math. Phys., 232, 223-277, 2003, [arXiv:math.OA/0006169].
7. R. Exel and J. Renault, AF-algebras and the tail-equivalence relation on Bratteli
diagrams,
preprint,
Universidade
Federal
de
Santa
Catarina,
[arXiv:math.OA/0307228].
113
List of new Ph.Ds in the area in the last 30 months
Danilo Royer, doctoral student at UNICAMP, a member of the group, will defend his PhD
thesis in the beginning of next year.
Finally, the Millenium Institute financed the visit of Professor Vaughan Jones who was in
Florianópolis from March 6 to 10, having given the talk "Two Subfactors" in the "Seminário
de Álgebras de Operadores" (see http://mtm.ufsc.br/~exel/seminario). 5. Descreva o
impacto que o apoio do Milênio teve em atividades científicas tais como confêrencias
organizadas e visitas de pesquisadores nacionais e internacionais. As mentioned,
Professor Vaughan Jones visited Florianópolis with support of the Instituto do Milênio. As
is well known, professor Vaughan Jones is among the greatest specialists in the area of
Operator Algebras and his visit to Florianópolis had a great impact in the sense of
motivating the members of the Seminar. Moreover we kicked off a joint project to study
the crossed product of the Temperley-Lieb algebra by the Shift endomorphism.
114
The research in Partial Differential Equations has made significant progress in the past
thirty months, with substantial improvement, both qualitative and quantitative, on its
publication record, in the conclusion of doctoral dissertations, in the implementation and
maturation of research and graduate education on developing institutions, and in the
intensification of the scientific exchange between researchers from Brazilian institutions
and their colleagues from abroad. The Millenium Institute has played a crucial role in this
progress.
Among the broad research lines in Partial Differential Equations, we highlight linear
equations, nonlinear evolution equations and nonlinear elliptic equations as areas of
particularly well developed activity, with large research production and with consolidated
and geographically well-distributed groups. The progress attained in this period will be
explored in what follows.
Scientific Meetings
1. II Workshop in Partial Differential Equations and Svereal Complex Variables, August 4
to 8, 2003, Serra Negra, SP. This meeting is now part of an international conference
cycle occurring every two years in Brazil, and alternating between the United States
and the People's Republic of China in the off years. The last such meeting took place
in Wuhan, PRC, in July 2004.
2. Colóquio Paraense de Matemática, December 2003 at the Federal University of Pará,
in Belém, PA. In this meeting, aside from sections on research presentation, there
were outreach lectures and discussion panels.
3. Milênio Workshop em Equações Elípticas, January 2004, João Pessoa, PB. This
meeting was co-organized by the PDE Groups at the Federal Universities at João
Pessoa and Campina Grande and was attended by the local community in PDE, as
well as researchers from other institutions. This stimulated local research through the
conclusion of ongoing reserch efforts as well as the formulation of new projects.
4. IV and V Workshops in Nonlinear Differential Equations, November 2002 and June
2004, Campinas, SP. Both these meeting were part of a series of events that begun
within the context of an international cooperation and exchange agreement between
Brazil and Italy and have been gaining in scope since. The V Workshop was held in
honor of the 70th birthday of Djairo Guedes de Figueiredo and included 43 talks by
researchers from outside Brazil.
5. I Escola Brasileira de Equações Diferenciais; June 2003, Campinas SP. Aside from
technical communications, by researchers from Argentina, Brazil and Chile, this event
included three minicourses, one in each of the three broad research lines mentioned
above. The second `Èscola'' is scheduled to take place in 2006, in IMPA.
6. Summer School in Differential Equations; This is an annual event held in S. Carlos, SP
and organized by the differential equations group at the ICMC-USP and whose
purpose is to promote the interaction between researchers in the field working in S.
Carlos and nearby institutions.
115
7. Symposium on Scattering and Spectral Theory; August 11 to 22 2003, Recife, PE. This
meeting was attended by specialists in Scattering Theory both from Brazil and abroad,
as well as graduate students.
8. Workshop em Equações Diferenciais: Teoria, Computação e Aplicações; July 21 to 25
2003, Rio de Janeiro, RJ. This is a large meeting occurring every two years at IMPA,
with strong international participation, on theoretical and computational aspects of
certain kinds of PDE.
Scientific Exchange
There has been a substantial increase in the scientific exchange both among researchers
in Brazil and between researchers in Brazil and abroad, stemming from visits of short
duration. This intensified exchange has resulted in an increment in collaborations leading
to publication of joint articles in international journals. Researchers from Belgium, Chile,
PRC, United States, France, India and Italy, among others, have maintained ongoing
collaboration with researchers from Brazil. The developing institutions have particularly
benefited from this intensified scientific exchange, as can be attested by their improved
publication record.
Reciprocal Contributions from Other Countries
One evidence of the increasing recognition Brazilian science has been achieving in the
field of Partial Differential Equations is the growing number of reciprocal financing of joint
research projects, with foreign institutions funding travel expenses for the visit of foreign
researchers to Brazil, or funding the local expenses of Brazilian researchers travelling
abroad.
Publications
As can be seen from the individual reports by organizers of the Millenium Institute
activities, there has been substantial improvement, both in quantity and in quality, of the
scientific output in the field of Partial Differential Equations by Brazilian researchers. This
increased productivity has been felt both in the established and in the emerging
institutions. We attribute this improvement to the talent of the young scientists coming out
of the graduate programs in the area in Brazil, to the intensification of the scientific
exchange of Brazilian researchers from different institutions among themselves and with
foreign distinguished colleagues and to a broadened horizon of planning for scientific
activities, brought about by the Millenium Institute.
Formation of Human Resources
The programs of scientific internships for undergraduates (IC) and MSc have provided a
well qualified pool of applicants to PhD level programs, which in turn has resulted in
increases in the number and improvements in the quality of doctoral dissertations.
Furthermore, post-doctoral internship programs taking place before a young researcher
settles in a permanent position have been contributing to the consolidation of the career of
the young PhDs.
116
The activities of the Millenium Institute have played an important part in instrumentalizing
the scientific development of our country, reaching many different levels of formation of
human resources, from IC to post-graduate research, going through the intermediate
stages. Among these activities connected with the Millenium Institute we highlight:
•
•
•
•
Supporting the needs of developing institutions in terms of IC grants, scientific
exchange, bibliographic material and computational infrastructure. In general, these
institutions do not receive adequate support from other agencies.
Supporting scientific exchange between established institutions and centers of
research outside Brazil, especially in the rest of Latin America.
Supporting IC and postdoctoral grant programs.
Financing national and international events as listed above.
The agility in the allocation and disbursement of financial resources on the part of the
Millenium Institute makes it possible to do broad medium term planning of scientific
activities. Through this planning it becomes possible to optimize the benefits accrued. For
example, visits of well-known foreign researchers are coordinated in such a way that
several institutions benefit from one trip.
The activity group in Partial Differential Equations has made significant progress in the
past thirty months, with substantial improvement, both qualitative and quantitative, on its
publication record, with the conclusion of doctoral dissertations, with the implementation
and maturation of research and graduate education on developing institutions, and with
the intensification of the scientific exchange between researchers from Brazilian
institutions and their colleagues abroad.
The creation of the Millenium Institute has played a crucial role in this progress by making
it possible to develop global strategic planning of scientific activities including meetings, IC
and Postgraduate programs and support to developing institutions in terms of bibliographic
and computational infrastructure.
1. A.P. Bergamasco, P. D. Cordaro and G. Petronilho, Global solvability for a class of
complex vector Fields on the two-torus, Comm. P.D.E., 29, 785-819, 2004.
2. Abreu, Eduardo Cardoso de, Furtado, Frederico and Felipe Pereira, On the numerical
simulation of three-phase reservoir transport problems. Transport Theory and
Statistical Physics, 2004.
3. Arrieta, J. M. and Carvalho, A.N.; Neumann Boundary Value Problems: Continuity of
Attractors with Respect to Domain Perturbations, Journal of Differential Equations,
199(1), 143-178, May 2004.
4. Artus, Vincent, Furtado, Frederico, Notinger, Benoit and Felipe Pereira, Stochastic
Analysis of Two-Phase Immiscible Flow in Stratified Porous Media. Computational and
Applied Mathematics, 2004.
5. Bruining, J., and Marchesin, D., Nitrogen and Steam Injection in a Porous Medium with
Water, Transport in Porous Media, 2004.
6. Bruining, J., Marchesin, D., and S. Schecter, Steam Condensation Waves in WaterSaturated Porous Rock, Qualitative Theory of Dynamical Systems, 2004.
117
7. Bruining, J., van Duijn, C. J., and Marchesin, D., Steam Injection into Water-Saturated
Porous Rock, Computational and Applied Mathematics, 2004.
8. D.G. de Figueiredo, M. Girardi and M. Matzeu, Semilinear elliptic equations with
dependence on the gradient via Mountain-pass techniques, Differential and Integral
Eq., 17, 119-126, 2004.
9. Felipe Pereira, Murad, Márcio Arab and Frias, Diego. Stochastic Computational
Modeling of Highly Heterogeneous poro-elastic Media with Long-Range Correlations,
International Journal for Numerical and Analytical Methods in Geomechanics, 28(1), 12, 2004.
10. Frias, D. and M. A. Murad and F. Pereira, Stochastic Computational Modeling of Highly
Heterogeneous Poroelastic Media with Long-Range Correlations International, Journal
for Numerical and Analytical Methods in Geomechanics, 28, 1-32, 2004.
11. Furtado, Frederico and Felipe Pereira, On the scale up problem for two-phase flow in
petroleum reservoirs, Cubo - Revista de Matemática, 2004.
12. Hildebrando M. Rodrigues and Joan Solà-Morales, Linearization of class C1 for
contractions on Banach spaces, J. Differential Equations, 201, 351-382, 2004.
13. Linares, Felipe and Corcho, A. Well-posedness for the Debye-Schrödinger equation,
Contemporary Mathematics. Amer. Math. Soc., 2004.
14. Linares, Felipe and J. Ortega. On the controllability and stabilization of the linearized
Benjamin-Ono equation, ESAIM: COCV, 2004.
15. Linares, Felipe and Panthee, M., On the Cauchy problem for a coupled system of KdV
equations, Comm. Pure and Applied Analysis, 2004.
16. Marchesin, D., Plohr, B. J., and Schecter, S., Computation of Riemann Solutions using
the Dafermos Regularization and Continuation, Discrete and Continuous Dynamical
Systems 10, 965-986, 2004.
17. Moyne, C. and M. A. Murad, Macroscopic Modeling of Cartilage: Mixture Theory
Versus Homogenization, Biorheology, 41(3-4), 215-222, 2004.
18. P. Cordaro and X. Gong, Normalization of complex-valued planar vector Fields which
degenerate along a real curve, Advances in Mathematics, 184, 89-118, 2004.
19. A. Moyne and M. A. Murad, Macroscopic Behavior of Swelling Porous Media derived
from Micromechanical Analysis, Transport in Porous Media, 50(1), 127-151, 2003.
20. A. Nachbin and K. Solna, Apparent diffusion due to orographic microstructure in
shallow waters, Phys. Fluids, 15(1), 66-77, 2003.
21. A. Nachbin, A terrain-following Boussinesq system, SIAM J. Appl. Math., 63(3), 905922, 2003.
22. Bergamasco, W. Nunes and S. Zani, Global properties of a class of overdetermined
systems, J. Funct. Anal., 200, 31-64, 2003.
23. Carvalho, A.N. and Gentile, C.B., Asymptotic Behavior of Nonlinear Parabolic
Equations with Monotone Principal Part, Journal of Mathematical Analysis and
Applications 280(2), 252-272, 2003.
24. Claudianor O. Alves and D.G. de Figueiredo, Nonvariational Elliptic Systems via
Galerkin Methods, Function Spaces, Differential Operators and Nonlinear Analysis
(The Hans Triebel Anniversary Volume), Birkhauser, 47-57, 2003.
118
25. D.G. de Figueiredo and Yang Jianfu, On a Semilinear Elliptic Problem Without (PS)
Condition, Journal of Differential Equations, 187, 412-428, 2003.
26. D.G. de Figueiredo and Yanheng Ding, Strongly Indefinite Functionals and Multiple
Solutions of Elliptic Systems, Transactions of the American Mathematical Society, 355,
2973-2989, 2003.
27. D.G. de Figueiredo, J.-P. Gossez and P. Ubilla Local Superlinearity and Sublinearity
for Indefinite Semilinear Elliptic Problems, J. Funct. Anal., 199, 452-467, 2003.
28. Douglas Jr, Jim, Frias and Diego, N. Henderson, Felipe Pereira. Simulation of singlephase multicomponent flow problems in gas reservoirs by Eulerian-Lagrangian
techniques, Transport in Porous Media, 50(3), 307-342, 2003.
29. Frid, Hermano and Chen, G.Q., Extended divergence-measure fields and the Euler
equations for gas dynamics, Communications in Mathematical Physics, 236(2), 251280, 2003.
30. Frid, Hermano. A quasilinear parabolic system for three-phase capillary flow in porous
media, SIAM Journal of Mathematical Analysis, 35(4), 1029-1041, 2003.
31. Frid, Hermano. Asymptotic stability of Riemann solutions for a class of multi-D viscous
systems of conservation laws, Archive Rat. Mech. Anal., 2003.
32. Frid, Hermano; Bürger, R. and Karlsen, K., On a free boundary problem for a strongly
degenerate quasilinear equation with an application to a model of pressure filtration.
SIAM Journal of Mathematical Analysis, 34(3), 611-635, 2003.
33. Frid, Hermano; Jabin, P. and Perhame, B., Global Stability of Steady Solutions foa a
Model in Virus Dynamics, ESAIM: Mathematical Modelling and Numerical Analysis,
37(4), 709-723, 2003.
34. Furtado Frederico and Felipe Pereira. Crossover from nonlinearity controlled to
heterogeneity controlled mixing in two-phase porous media flows, Computational
Geosciences, 7, 115-135, 2003.
35. Isabel S. Labouriau and Hildebrando M. Rodrigues, Synchronization of Coupled
Equations of Hodgkin-Huxley Type, Dynamics of Continuous, Discrete and Impulsive
Systems, Ser.A, 10(1-3), 463-476, 2003.
36. J.M.B. do O’, P. Ubilla, Multiple Solutions for a class of Quasilinear Elliptic Problems,
Proc. Edinburg Math. Soc., 46, 159-168, 2003.
37. J.P. Fouque and A. Nachbin, Time-reversed refocusing of surface water waves, SIAM
Multiscale Modeling and Simulation, 1(4), 609-629, 2003.
38. J.P. Fouque J. Garnier and A. Nachbin, Time reversal for dispersive waves in random
media, SIAM J. Appl. Math., 2003.
39. Linares, Felipe and Biagioni, H., Ill-posedness for the Zakharov system with
generalized nonlinearity, Proceedings of the Americam Mathematical Society, 131(10),
3113-3121, 2003.
40. Linares, Felipe and Biagioni, H., Well-posedness results for the modified ZakharovKuznetsov equation, Progress in Nonlinear Differential Equations, 54, 181-190, 2003.
41. Linares, Felipe and X. Carvajal. Paredes A Higher order nonlinear Schroedinger
equation with variable coefficients, Differential and Integral Equations, 16, 1111-1130,
2003.
119
42. Linares, Felipe; G. Fonseca and G.Ponce Global existence for the critical generalized
KdV equation, Proc. Amer. Math. Soc., 131(6), 1847-1855, 2003.
43. M. Cuesta, D.G. de Figueiredo and P.N. Srikanth, On a resonant-superlinear elliptic
problem, Calculus of Variations and Partial Differential Equations, 17, 221-233, 2003.
44. Marchesin, D. and Schecter, S., Geometric Singular Perturbation Analysis of Oxidation
Heat Pulses for Two-Phase Flow in Porous Media, 2003.
45. Marchesin, D. and Schecter, S., Oxidation Heat Pulses in Two-Phase Expansive Flow
in Porous Media, Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 54, 4883, 2003.
46. S. Berhanu and J. Hounie, On boundary regularity for one-sided locally solvable vector
Fields, Indiana Univ. Math. J., 52, 1447-1477, 2003.
47. S. Berhanu and J. Hounie, Traces and the F. and M. Riesz theorem for vector Fields,
Ann. Inst. Fourier, 53, 1425-1460, 2003.
48. Sarkis, Marcus and Tu, Xuemin. Singular Function Mortar Finite Elements Methods,
Computer Methods in Applied Mathematics, 3 (1), 2003.
49. Sarkis, Marcus; Xiao-Chuan, Cai and Dryja, Maksymilian. Restricted Additive Schwarz
Preconditioners with Harmonic Overlap for Symmetric Positive Definite Systems. In:
SIAM Journal on Numerical Analysis, 41, 1209-1231, 2003.
50. Zubelli, J.P. and Castellano-Perez, L.O., On the Inverse Problem for Scattering of
Electromagnetic Radiation by a Periodic Structure, Studies in Applied in Applied
Mathematics, 111(2), 115-166, 2003.
51. Zubelli, J.P. and Fabio Chalub, Matrix Bispectrality and Huygens' Principle for Dirac
Operators, Contemporary Mathematics, 2003.
52. Zubelli, J.P., Marabini, R., Sorzano, C.O.S. and Herman, G.T., Three-dimensional
reconstruction by Chahine's method from electron microscopic projections corrupted by
instrumental aberrations. Inverse Problems, Bristol, UK, 19(4), 933- 949, 2003.
53. Almeida, C. G., Douglas Jr, Jim and Felipe Pereira. A new characteristics-based
numerical method for miscible displacement in heterogeneous formations.
Computational and Applied Mathematics, 22, 573-605, 2002.
54. Boletim da Sociedade Brasileira de Matemática, 32(3), 237-270, 2002.
55. Carvalho, A.N. and Cholewa, J.W., Attractors for Strongly DampedWave Equation with
Critical Nonlinearities, Pacific Journal of Mathematics, 207(2), 2002.
56. Carvalho, A.N. and Cholewa, J.W., Local Well Posedness for Strongly Damped Wave
Equation with Critical Nonlinearities, Bulletin of the Australian Mathematical Society,
66, 443-463, 2002.
57. Claudianor O. Alves and D.G. de Figueiredo, Nonvariational Elliptic Systems, Discrete
and Continuous Dynamical Systems, 8, 289-300, 2002.
58. Cordaro, P., Approximate solutions in locally integrable structures, Fields Institute
Communications Volume: Differential Equations and Dynamical Systems, 31, 97-112,
2002.
59. D. Frias, M. A. Murad and F. Pereira, Computational Modeling of Reservoir
Compaction due to Fluid Withdrawal, Computational and Applied Mathematics, 21(2),
607-629, 2002.
120
60. D.G. de Figueiredo and Yanheng Ding, Solutions of a nonlinear Schrodinger equation,
Discrete and Continuous Dynamical Systems, 8, 563-584, 2002.
61. D.G. de Figueiredo, J.M. do O’ and B. Ruf, On an inequality by Trudinger and Moser
and related Nonlinear Elliptic Equations, Comm. Pure Appl Math, 55, 135-152, 2002.
62. Frias, Diego, Murad, M. A. and Felipe Pereira, Stochastic Computational Modeling of
Reservoir Compaction Due to Fluid Withdrawal, Computational and Applied
Mathematics, 22, 607-629, 2002.
63. Frid, Hermano, Decay of Almost Periodic Solutions of Conservation Laws, Archive for
Rational Mechanics and Analysis, 161(1), 43–64, 2002.
64. Frid, Hermano, Uniqueness and Stability of Riemann Solutions With Large Oscillation
in Gas Dynamics, 2002.
65. Frid, Hermano; G.Q. Chen and Y. Li, Communications in Mathematical Physics,
228(2), 201–207, 2002.
66. Frid, Hermano; Shelukhin, V., A Quasilinear Parabolic System for Three Phase
Capillary Flow in Porous Media, SIAM Journal on Mathematical Analysis, 2002.
67. G. Petronilho, Global solvability and simultaneously approximable vectors, J. of
Differential Equations, 184, 48-61, 2002.
68. Himonas, A. and Petronilho, G., Propagation of regularity and global hypoellipticity,
Michigan Math. J., 50, 471-481, 2002.
69. Hounie, J. and E. da Silva, A Similarity Principle for Locally Solvable Vector Fields, J.
Math. Pures Appl., 81, 715-746, 2002
70. Hounie, J., Fifty years of local solvability, Matemática Contemporânea, 23, 1-17, 2002.
71. Linares, Felipe and H. Biagioni, Ill-Posedness For the Zakharov System with
Generalized Nonlinearity, Proceedings of AMS, 2002.
72. Linares, Felipe and H. Biagioni, Well-Posedness Results for the Modified ZakharovKuznetsov Equation, Progress in Nonlinear Differential Equations, 2002.
73. Linares, Felipe and M. Scialom, On Generalized Benjamin Type Equations, Discrete
and Continuous Dynamical Systems, 2002.
74. Linares, Felipe, On the Schrödinger-Boussinesq Equation. Differential and Integral
Equations, 2002.
75. Linares, Felipe; A. Navas, J. Angulo, J. Bona and M. Scialom. Scaling, Stability and
Singularities for Nonlinear, Dispersive Wave Equation: The Crical Case, Nonlinearity,
15, 759-786, 2002.
76. Linares, Felipe; G. Fonseca and G. Ponce. Global Well-Posedness for the Critical
Generalized Kdv Equation. Proceedings of AMS, 2002.
77. M.A. Murad and C. Moyne, Micromechanical Computational Modeling of Expansive
Porous Media, C.R. Mecanique, 330, p.865-870, 2002.
78. Marchesin, D., Azevedo, A., Plohr, B. J. and Zumbrun, K., Capillary Instability in
Models for Three-Phase Flow, Zeitschrift für Angewandte Mathematik und Physik
(ZAMP), 53(5), p.713-746, 2002.
79. Marchesin, D., Bedrikovetsky, P., Tran, K., Broek, W., Rezende, E., Siqueira, A., Serra,
A. and Shecaira, F., Damage Characterization of Deep Bed Filtration,
121
80. Marchesin, D., da Mota, J. C., and Dantas, W. B., Combustion Fronts in Porous Media,
SIAM Journal on Applied Mathematics, 62(6), 2175-2198, 2002.
81. Marchesin, D., da Mota, J. C., de Souza, A. J., and Teixeira, P. W., A Simplified
Oxidation Model for Two-Phase Flow in Porous Media, Engenharia Térmica, Edição
Especial, 2, 9-14, 2002.
82. Marchesin, D., Santos, R. W., Gundelach, B. and Valério, J., Magnetocardiographic
Location of Rotating Spiral Electrochemical Waves, Matemática Contemporânea,
22(1), 97-112, 2002.
83. Moyne, C. and M. A. Murad, Electro-Chemo-Mechanical Coupling in Swelling Clays
Derived from a Micro/Macro Homogenization Procedure, International Journal of Solids
and Structures, 39, 6159-6190, 2002.
84. Rafael José Iório Junior, Unique Contimation Principles for the Benjamin-Ono
Equation. Aceito para publiação em Differential and Integral Equations, 2002.
85. Rafael José Iório Junior, Unique Continuation Principles for Some Equatins of
Benjamin-Ono Type. Proceedings of the Workshop on Non-Linear Differential
Equations, Bergamo, Italia, 2002.
86. S. Berhanu and J. Hounie, On boundary properties of solutions of complex vector
Fields, J. Funct. Anal., 192, 446-490, 2002.
87. Sarkis, Marcus. A Coarse Space for Elasticity: Partition Of Unity Rigid Body Motions
Coarse Space. Aceito para publicação em Applied Mathematics and Scientific
Computing, Eds. Z. Drmac et al., Kluwer Academic/Plenum Plublishers, 2002.
88. Sarkis, Marcus. Domain Decomposition: Schwarz Methods. Aceito para publicação em
Applied Mathematics and Scientific Computing, eds. Z. Drmac et al, Kluwer Academic,
Plenum Plublishers, 2002.
89. Sarkis, Marcus. Partition of Unity Coarse Spaces and Schwarz Methods with Harmonic
Overlap Lecture. Notes in Computational Science and Engineering, Eds L. Pavarino
and A. Toselli, Springer-Verlag, 23, 75-92, 2002.
90. Sarkis, Marcus. Partition of Unity Coarse Spaces, Fluid Flows and Transport In Porous
Media, Mathematical And Numerical Treatment. Contemporary Mathematics, 295,
445–456, 2002.
91. Sarkis, Marcus; X-C. Cai and Dryja, M. A Restricted Additive Schwarz Preconditioner
with Harmonic Overlap For Symmetric Positive Definite Linear Systems, SIAM
Numerical Analysis, 2002.
92. SPE 74664, sinopse, Journal of Petroleum Engineering, p.51, March 2002.
93. Frid, Hermano; Shelukhin, V., Boundary Layers in Parabolic Perturbations of Scalar
Conservation Laws. Zeitschrift fur angewandte Mathematik und Physik-ZAMP, 2002.
94. Frid, Hermano Burger, H. and Karlsen, K., On a Free Boundary Problem for a Strongly
Degenerate Quasilinear Equation with an Application to a Model of Pressure Filtration.
SIAM Journal of Mathematical Analysis, 2002.
95. Zubelli, J.P.; Pedroni, M. and Sciacca, V., On the Bi-Hamiltonian Theory for the Harry
Dymequation. Theoretical and Mathematical Physics, 133(2), .1583-1595, 2002.
122
96. Zubelli, J.P. and L.O. Castellano Perez, On the Inverse Problem for Scattering of
Electromagnetic Radiation by a Periodic Structure. Studies in Applied Mathematics,
2002.
Accepted/Submitted
1. A.Bergamasco, W. Nunes and S. Zani, Prescribing analytic singularities for solutions of
a class of vector fields on the torus, Trans. Amer. Math. Soc., 2004.
2. A.Himonas and G. Petronilho, On C1 and Gevrey regularity of sublaplacians,
Transactions of Amer. Math. Soc., 2004.
3. A.Himonas and G. Petronilho, On Gevrey regularity of globally C1 hypoelliptic
operators, Transactions of Amer. Math. Soc., 2004.
4. Berhanu and J. Hounie, The F. and M. Riesz property for vector fields, Contemporary
Math., 2004.
5. Carvalho, A.N. and Primo M.R.T., Spatial Homogeneity in Parabolic Problems with
Nonlinear Boundary Conditions, Communication in Pure and Applied Analysis, 2004.
6. Carvalho, A.N. and Dlotko, Tomasz, Partially Dissipative Systems in Uniformly Local
Spaces, Colloquium Mathematicum, 2004.
7. D.G. de Figueiredo and B. Sirakov, Liouville type theorems, monotonicity results and a
priori bounds for positive solutions of elliptic systems, to appear
8. D.G. de Figueiredo and O.H. Miyagaki, Multiplicity of non-radial solutions of critical
elliptic problems in an annulus, Proceedings of the Royal Math Soc Edinburg, 2004.
9. D.G. de Figueiredo, J.M.B. do O’ and B. Ruf, Critical and Sub-critical Systems in
dimension two, Indiana University Math Journal, 2004.
10. D.G.Costa, D.G. de Figueiredo and Yang Jianfu, On Best Constants for Limiting
Embeddings of Fractional Sobolev Spaces, Proc of AMS, 2004.
11. Frid, Hermano and Perepelitsa, M., Spatially periodic solutions in relativistic isentropic
gas dynamics, Communications in Mathematical Physics, 2004.
12. Frid, Hermano and Shelukhin, V., Initial Boundary Value Problems for Quasilinear
Parabolic System in Three-Phase Capillary Flow in Porous Media, SIAM Journal of
Mathematical Analysis, 2004.
13. Frid, Hermano. Asymptotic Stability of Riemann Solutions for a Class of Multi-D
Viscous Systems of Conservation Laws, Arch. Rat. Mech. Anal, 2004.
14. Asymptotic stability of Riemann solutions of multi-D systems of conservation laws with
symmetric nonlinearities, Journal of Hyperbolic Differential Equations, 2004
15. Hildebrando M. Rodrigues and Joan Solà-Morales, Smooth Linearization for a Saddle
on Banach spaces, JDDE, 2004.
16. J. Hounie, A note on the Mihlin-Hormander multiplier theorem, Comunications in
Applied Analysis, 2004.
17. J.M.B. do O’, S. Lorca and P. Ubilla, Local Superlinearity for elliptic systems involving
parameters, Journal of Differential Equations, 2004.
18. J.R. dos Santos Filho, Injective Mappings and Solvable Vector Fields of Euclidean
Spaces, Topology and its Applications, 2004.
123
19. L.A. Carvalho dos Santos and J. Hounie, Estimates for the Poisson kernel and Hardy
spaces on compact manifolds, J. of Math. An. and Appl., 2004.
20. P. Cordaro and N.Hanges, Impact of lower order terms on amodel PDE em two
variables, Contemporary Mathematics, 2004.
21. Zubelli, J.P. and F. Chalub, Huygens' Principle, Dirac Operators, and Rational
Solutions of the AKNS Hierarchy, Mathematical Physics, Analysis and Geometry,
2004.
22. Zubelli, J.P. and F. Chalub, Matrix Bispectrality and Huygens' Principle for Dirac
Operators, Contemporary mathematics, 2004.
23. Abreu, E. A. M. and Carvalho, A.N., Lower Semicontinuity of Attractors for Parabolic
Problems with Dirichlet Boundary Conditons in Varying Domains, Notas do ICMC/USP
- Série Matemática, 148, Submitted for publication.
24. Carvalho, A.N. and Bruschi, S. M., Continuity of Attractors for a Perturbed Hyperbolic
Problem, Notes ICMC/USP, Serie Mathematics, 122, Submitted for publication.
25. Carvalho, A.N. and Bruschi, S. M., Upper semicontinuity of Attractors for the
discretization of a strongly damped wave equation, Notes ICMC/USP, Serie
Mathematics, 167, Submitted for publication.
26. Carvalho, A.N. and Cholewa, J.W., Continuation and asymptotics to semilinear
parabolic equations with critical nonlinearities, Notes ICMC/USP, Serie Mathematics,
196, Submitted for publication.
27. Carvalho, A.N. and Lozada-Cruz, G, Paterns in Parabolic Problems with Nonlinear
Boundary Conditions, Notes ICMC/USP, Serie Mathematics, 123, Submitted for
publication.
28. Carvalho, A.N. and Piskarev S., A general approximation scheme for attractors of
abstract parabolic problems, Notes ICMC/USP, Serie Mathematics, 197, Submitted for
publication.
29. Carvalho, A.N.; Lozada-Cruz, G. and Primo M.R.T., Spatial homogeneity in
atmospheric problems, Preprint.
30. J.M.B. do O’, S. Lorca and P. Ubilla, Multiparameter elliptic equations in annular
domains, to appear.
Books
1. Abreu, Eduardo Cardoso de, Furtado Frederico, Marchesin, Dan, Felipe Pereira.
Transitional waves in three-phase flow in heterogeneous formations, In: Computational
Methods in Water Resources, ed. Elsevier, 2004.
2. Douglas Jr, Jim, Felipe Pereira, Roman, L. C. Algorithmic aspects of a locally
conservative eulerian-lagrangian method for porous media flow In: Mathematical and
Numerical Modeling for Subsurface and Surface Problems ed. Amsterdam, Elsevier, II,
971-978, 2002.
3. Felipe Pereira, Almeida, C. G., Roman, L. C., Douglas Jr, Jim, Yeh, Li Ming.
Algorithmic aspects of a locally conservative eulerian-lagrangian method for transportdominated diffusive systems In: Fluid flow and transport in porous media: mathematical
and numerical treatment (CONM Book Series) ed. American Mathematical Society,
2002, 295, p.37-48.
124
Mathematical Economy and Finances
The main topics of research in mathematical economics in the context of IM-AGIMB are
general equilibrium with incomplete markets and bankruptcy, asymmetric information
problems without the single-crossing property, equilibria in security markets, collaterals,
models with a supra national currency.
Due to the great interest of both the public and private sectors, the area of Mathematical
Economics is important for the development of the country, but is to be mentioned a main
difficulty for the stablishment of a sufficient large scientific-academic community in the
area. This is basically due to the fact that the young scientists are offered better salaries
by the private and public sectors or by academic institutions abroad. Even so, the number
of Ph.D´s formed in the country is increasing as well as the amount of articles published in
the best journals, notestandingly a proeminent role-played by the former IMPA´s students.
The role of IM-AGIMB has been essential for the clear success of the area in Brazil in
recent years, for allowing the planning of an important workshop and of high level scientific
cooperation.
Complete Works in Proceedings of Events
1. Araujo, A., Plenary Session: Rolf Mantel Lecture. Latin American Meeting of the
Econometric Society, 2003, Panama. Annals of Latin American Meeting of the
Econometric Society, 2003.
2. Araujo, A., Do Dividend Signaling without Single-Crossing Property. 24th Brazilian
Encounter of Econometrics, 2002, Friburgo. Annals of the 24th Brazilian Encounter of
Econometrics, 2002.
3. Araujo, A. and Moreira, H., Non-Monotone Insurance Contracts and their Empirical
Consequences. 57th European Meeting of the Econometric Society, 2002, Venice.
Annals of 57th European Meeting of the Econometric Society, 2002.
4. Araujo, A., Puree Strategy Equilibria and Monotonic Auctions. 24th Brazilian encounter
of Econometria, 2002, Friburgo. Annals of the 24th Brazilian Encounter of
Econometrics, 2002.
5. Araujo, A., Pure Strategy Equilibria in Auctions: New Results. First Brazilian Workshop
of The Game Theory Society, 2002, São Paulo. Annals of First Brazilian Workshop of
Game Theory, 2002.
Complete articles published in Journals
1. Araujo, A., Rock, V.F. and Monteiro, P.K., Equilibria in Reflexive Banach Lattices with
the Continuum of Agents, Economic Theory, 2004.
2. Araujo, A. and León, M.S., Speculative attacks on Debts and Dolarization, Revista
Brasileira de Economia, Rio de Janeiro, Brazil, 56(1), 7-46, 2002.
3. Araujo, A. and Páscoa, M., Bankruptcy in a Model of Unsecured Claims. Economic
Theory, United States, 20 (3), 455-481, 2002.
125
4. Araujo, A., Páscoa, M. and Martinez, J.P.T., Collateral avoids Ponzi schemes in
incomplete markets. Econometrica, United States, 70(4), 1613-1638, 2002.
Chapters of published books
1. Araujo, A. and Páscoa, M., Default and Collateral: New Applications of General
Equilibrium to Finance, Cambridge, 2004.
2. Araujo, A. and Maldonado, W., Learning in intemporal equilibrium models and sunspot
case, F. Petri and F. Hahn Routledge Taylor and Francis (org.), General Equilibrium:
Problems and Prospects, New York, 58-73, 2003.
3. Araujo, A. and León, M., Monetary Regimes and Mercosur, Pierre Van Gives; VIÑALS,
José. (org.), Regional Integration in Europe and Latin América, Monetary and
Financial Aspects, Ashgate Publishing Limited. Hampshire, 1, 145-168, 2003.
Other types of bibliographical production
1. Araujo, A., Moreira, H. and Tsuchida, M., Do dividends signal more earnings? Getulio
Vargas Foundation, RJ, 2004. (Ensaios Econômicos, 524).
2. Araujo, A., Moreira, H. and Tsuchida, M., The Trade between incentives and
endogenous risk, Getulio Vargas Foundation, RJ, 2004 (Economic Rehearsals, 523).
3. Araujo, A., The Laws of Failure: An Economic Approach, Getulio Vargas Foundation,
RJ, 2003. (Economic Rehearsals, 474).
4. Araujo, A., Barbachan, J.S.F. and Páscoa, M., Endogenous Collateral, Getulio Vargas
Foundation, RJ, 2003. (Economic rehearsals, 511).
5. Araujo, A., Rocha, V.F. and Monteiro, P.K., Equilibria in Security Markets with a
Continuum of Agents, Getulio Vargas Foundation, RJ, 2003. (Economic Rehearsals,
513).
6. Araujo, A. and Moreira, H., Non-Monotone Insurance Contracts and their Empirical
Consequences, Getulio Vargas Foundation, RJ, 2003. (Economic rehearsals, 512).
7. Araujo, A. and León, M., Speculative Attacks on Debts and Optimum Currency Area: A
Welfare Analysis, Getulio Vargas Foundation, RJ, 2003. (Economic rehearsals, 514).
8. Araujo, A. and León, M., Speculative Attacks on Debts, Dollarization and Optimum
Currency Areas, Getulio Vargas Foundation, RJ, 2002. (Economic rehearsals, 446).
Ph.Ds.
1. Tsuchida, Marcos Hiroyuki, Essays on Asymmetric Information Problems without the
Single-Crossing Property: Applications to Corporate Finance, Getúlio Vargas
Foundation, RJ, 2003.
2. León, Márcia Saraiva, Speculative attacks on Debts and Monetary Aspects (Regimes),
Getúlio Vargas Foundation, RJ, 2002.
3. Martinez, Juan Pablo Torres, Infinite Horizon Incomplete Markets: Equilibrium, Default
and Bubbles, Institute of Pure and Applied Mathematics. 2002
126
4. Villegas, Alvaro José Riascos, Three Essays on Monetary and Fiscal Policy in General
Dynamic Equilibrium Models, Institute of Pure and Applied Mathematics, 2002.
Contribution and Impact
The Millennium Institute was essential for the development of the area in the last years. In
this sense, the promotion of the Workshop in Mathematical Economics, with the
participations of several researchers' of great international reputation, was very important.
The Workshop in Mathematical Economics which took place in IMPA on July 22-24 was a
Satellite Conference of 2002 Latin American Meeting of the Econometric Society that was
held at the campus of Fundação Getúlio Vargas (FGV-EAESP) on July 25-27, 2002. 25 of
its participants also took part in the meeting in IMPA and among them Professors James
Heckman (University of Chicago) and Daniel McFadden (University of California,
Berkeley), both Nobel Prize winners in Economic Sciences.
In the Workshops in Rio and in São Paulo, editors of some of the most important journals
in Economics were present, such as: B.Cornet of the Journal of Mathematics Economics,
Myrna Wooders of Public Economic Theory, Vijay Krishna of the Game Theory and
Economic Behavior, Hervé Moulin and William Thomson of Mathematics Social of
Sciences. This shows a great interest in the Workshop.
The program consisted of invited and contributed papers that represent a broad spectrum
of theoretical and applied economics and econometrics.
Also important was the recent visit of Prof. Andreu Mas-Colell, of the Pompeu Fabra
University, promoted by IM-AGIMB. He is one of the best mathematical economists of the
present time. Prof. Mas-Colell taught at the Universities of Berkeley and Harvard and, later
on, went back to Spain. He is the author of several articles and monographs of enormous
scientific impact in the area and he is also a co-author of the main book-text of
Mathematical Economics that is used in practically all the major American and European
Universities Ph.D. programs. He was President of the Econometric Society and he is
Member of both the National and the American Academy of Sciences.
127
Probability
Summary of the main advancements during the last 30 months
During this period there was an intense research activity in various topics in theoretical
probability and applications, in special to statistical mechanics. It deserves to be
mentioned the success obtained in the study of disordered systems, in particular in the
treatment of random walks in random environments, and growth models out of equilibrium.
Special emphasis merits the results which have been obtained in the hydrodynamical
description of particle systems, perfect simulation, convergence of random trees to
structures such as the Brownian web, interfaces of competition, besides applications to
linguistics.
Research articles published or accepted 2002-2004
During the period, the members of the team have had around fifty research articles
published or accepted for publication and a book, edited by the Cambridge University
Press.
It follows the list of the works, which considered being the most important for the area. The
full list is found in the reports sent by the various work groups.
1. Ferrari, P. A., Landim, C. and Thorisson, H., Poisson trees, succession lines and
coalescing random walks, Annales de L'Institut Henry Poincaré, 40, 141-152, 2004.
2. Fontes, L. R. G., Isopi, M., Newman, C. M. and Ravishankar, K., The Brownian Web:
Characterization and Convergence, Annals of Probability, 2004.
3. Machado, F. P., Alves, O. and Ferreira, C. E., Estimates for the spreading velocity of
an epidemic model, Mathematics and Computers in Simulation, 2004.
4. Olivieri, E. and Vares, M.E., Large Deviations and Metastability, Cambridge Univ.
Press, Encyclopedia of Mathematics and its applications, 512p, 2004.
5. Ramirez, A. F. and Sidoravicius, V., Asymptotic behavior of boundary branching
random walks growth process, J. Europ. Math. Soc. JEMS, 6 (3), 293-334, 2004.
6. Sidoravicius, V. and Sznitman, A.S., Quenched invariance principles for walks on
clusters of percolations or among random conductances, Probab. Theory. Rel. Fields.,
129(2), 2004.
7. Abadi, M., Sharp error terms and necessary conditions for exponential hitting times in
mixing processes, Annals of Probability, 2003.
8. Abadi, M. Chazottes, J.R.; Redig, F.; Verbitskiy E., Exponential distribution for the
occurrence of rare patterns in Gibbsian random fields, Comm. Math. Phys, 2003.
9. Comets, F. and Popov, S., Limit law for transition probabilities and moderate deviations
for Sinai's random walk in random environment, Probability Theory and Related Fields,
126, 571-609, 2003.
10. Ferrari, P. A., Andjel, E. D. and Siqueira, A., Law of large numbers for the asymmetric
simple excusion process, Stochastic Processes and their Applications, 2003.
128
11. Garcia, N. and Motta, M.R., Perfect simulation for a stationary silo with absorbing
walls, Meth. Comp. Appl. Probab, 5, 109-121, 2003.
12. Machado, F.P. and Popov, S., Branching random walk in random environment on
trees, Stochastic Processes and their Applications, 106, 95-106, 2003.
13. Fernandez, R and Galves, A., Markov approximations of chains of infinite order, Bull.
Braz.Math.Soc., 33, 295-306, 2002.
14. Fontes, L. R., Schonmann, R. H. and Sidoravicius, V., Stretched exponential fixation in
stochastic Ising models at zero temperature, Comm. Math. Phys, 228(3), 495-518,
2002.
15. Kesten, H. and Sidoravicius, V., The spread of a rumor or infection in a moving
population, Annals of Probab. Math.PR/0312496.
Ph.Ds. Degree
1. Fernando Pigeard de Almeida Prado, 2004, IME-USP. Advisor: Vladimir Belitsky
2. Guillermo Tomás Tetzlaff, 2004, Departamento de Computacin, FCEyN, Universidad
de Buenos Aires. Advisor: Pablo Augusto Ferrari.
3. Leandro Pinto Pimentel, 2004, IMPA. Advisor: Vladas Sidoravicius.
4. Milton Jara, 2004, IMPA. Advisor: Claudio Landim.
5. Adriano Francisco Siqueira, 2003, IME-USP. Advisor: Luiz Renato Gonalves Fontes.
6. Bernardo Borges Nunes de Lima, 2003, IMPA, (Prêmio Aranda Ordaz). Advisor:
Vladas Sidoravicius.
7. Denise Duarte Scarpa Magalhães Alves, 2003, IME-USP. Advisor: Antonio Galves.
8. Glauco Valle da Silva Coelho, 2003, IMPA. Advisor: Claudio Landim.
9. Raquel Mariela Sued, 2003, IMPA, (Prêmio Aranda Ordaz). Advisor: Claudio Landim.
10. Valentim Sisko, 2003, IME-USP. Advisor: Pablo Augusto Ferrari.
How did the IM-AGIMB contributed to the achievement of the results in research, as
well on the formation of new researchers?
IM-AGIMB has promoted in an unprecedented way the participation of students in the
scientific life of the group in a very intense way. For instance, they were stimulated to
expose their work in the various scientific meetings, which were organized with the
presence of scientific leaderships in the related topics. This has guaranteed them to be
much more integrated in the efforts, which were happening, and to receive a wide but
constructive criticism of their work. Post-doctoral positions have also been crucial on that,
due to the exchange of experiences. In terms of the progress in mathematics research, the
conferences had a very positive effect together with the crucial impact that seems to have
come from the scientific visits, partially promoted by IM-AGIMB, which definitely allowed
the continuation and conclusion of scientific projects of much relevance to the field.
129
Impact which the support of IM-AGIMB had in the scientific activities as the
promoter of conferences and visits of researchers (national and international).
IM-AGIMB has been extremely important for the success of the following workshops and
conferences, for allowing its planning and implementation in an exceptional scientific level.
•
•
•
•
•
The Editions VI, VII and VIII Brazilian School of Probability Brazilian School of
Probability, happening in 2002 (Ubatuba, SP), 2003(Angra dos Reis, RJ) and 2004
(Ubatuba, SP) respectively.
Workshop Disorder, Percolation, Random Walks, 18-19 de fevereiro de 2002, IMPA,
Rio de Janeiro, Brasil.
Percolation, Particle Systems and Random Media, 12-17 de janeiro de 2004, Santiago
de Chile. (Evento realizado em colaboração da PUC de Santiago do Chile e do IMPA.)
Combinatorics, Probability and Computing, 12-14 de fevereiro, 2004, IMPA, Rio de
Janeiro, Brasil.
Brazilian Workshop on Mathematical Physics, 3-5 de março, 2004, IMPA, Rio de
Janeiro, Brasil.
IM-AGIMB has also been crucial for the participation of a large number of Latin-American
researchers and students in the last editions of the Brazilian School of Probability. This
was exactly one of our major difficulties before the IM-AGIMB. It has also allowed that
students already initiated in research and young researchers would attend the workshop
``Percolation, Particle Systems and Random Media", an occasion when they had the
opportunity not only to explain their own work, but also to learn from the informal and
formal discussions with some of the highest level specialists in the topic. The existence of
IM-AGIMB is, no doubt, profoundly changing the possibilities of interaction in Latin
America. Another example, besides the Workshop done in collaboration with PUC from
Santiago, is the "Encontro em Probabilidade e Estatística Matemática" which will happen
in Buenos Aires at the end of this September, as well as most of the flow of researchers
between Brasil, Uruguai, Argentina and Chile, which is visible in the scientific projects
which had been developed (as shown in the list of publications).
We plan to extend this interaction in the next "summer school at IMPA", with the
participation of a researcher from Universidad Nacional de Mexico, and also by a stronger
interaction with colleagues from Venezuela (Summer School in Merida, in September of
2005). This experience also offers to the students the opportunity to wide their vision of the
area beyond the research lines that are most developed in their own institution.
Concerning the collaboration through scientific visits, the results reported in the research
articles speak by themselves. Besides, there is an intense activity going on relative to
articles under preparation. The financial resources provided by other national sources has
also contributed much for the success of the scientific cooperation in the area.
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Petroleum Sciences
IM-AGIMB’s Impact
It is fair to say that IM-AGIMB was instrumental in promoting scientific interchange among
the small number of researchers in Brazil interested in mathematical aspects of petroleum
science, both by planning and promoting symposia and workshops and by supporting
mutual collaborative visits on short notice. It has fostered further scientific links between
these researchers and the international community.
In turn, these international links have been extremely beneficial to students in this area.
For instance, while there was 1 graduate student in this area at IMPA before IM-AGIMB,
there are now 8 students.
IM-AGIMB’s action improves considerably and complements the work of other agencies
that have been striving to involve mathematically minded scientists in activities with
significant economic and social relevance for the country. The basic concept of a Virtual
Institute of Excellence is a crucial new way to make concentrated scientific progress in
areas of prime importance to society.
Conceptual Progress
A better understanding of the several multiscale phenomena that occur in flow in porous
media has been reached, especially in the nonlinear scale-up problem in petroleum
reservoirs.
Progress has been made in understanding the wave structure of thermal flow in reservoirs,
which is important for the recovery of the existing untouched reserves of very viscous oil.
Scientific Events in the Area Supported by IM-AGIMB
1. Minisymposium on Petroleum Reservoirs and Aquifers, in the XXV National Congress
on Computational Mathematics, IPRJ, Nova Friburgo, September 16-19, 2002.
2. Second Symposium on Computational Modeling of Multiscale Phenomena, LNCC,
August 6-9, 2002.
3. VIII Workshop on Partial Differential Equations: Theory, Computation and Applications,
IMPA, July 21-25, 2003.
Scientific Visits Supported by IM-AGIMB
1. A. Mailybaev, Moscow State Lomonosov University, Russia, IMPA, March-June 2004.
2. J. Bruining, Technical University of Delft, The Netherlands, IMPA, September 2004.
3. A. Mailybaev, Moscow State Lomonosov University, Russia, IMPA, July-October 2003.
4. I.
Yucel Akkutlu, University of Alberta, Canada, IMPA, May-August 2002.
131
Doctoral Degrees in the Area
1. Vitor Manuel Martins de Matos, IMPA, April 2004. Riemann Problem for Two
Conservation Laws of Type IV with Elliptic Region. Advisor: Dan Marchesin (IMPA).
2. Jesus Alexei L. Obregon, COPPE - Department of Mechanical Engineering, 2003.
Micromechanical Modeling of Poroplasticity. Advisors: Marcio Murad (LNCC/MCT) and
Fernando Rochinha (PEM/COPPE).
Articles in the Area Promoted by IM-AGIMB
1. Bruining, J. and Marchesin, D., Nitrogen and Steam Injection in a Porous Medium with
Water, Transport in Porous Media, 2004.
2. Marchesin, D., Plohr, B. J. and Schecter, S., Computation of Riemann Solutions using
the Dafermos Regularization and Continuation, Discrete and Continuous Dynamical
Systems 10, 965-986, 2004.
3. Bruining, J., Marchesin, D. and S. Schecter, Steam Condensation Waves in WaterSaturated Porous Rock, Qualitative Theory of Dynamical Systems, 2003.
4. Bruining, J., van Duijn, C. J. and Marchesin, D., Steam Injection into Water-Saturated
Porous Rock, Computational and Applied Mathematics, 2003.
5. Marchesin, D. and Schecter, S., Oxidation Heat Pulses in Two-Phase Expansive Flow
in Porous Media, Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 54, 4883, 2003
Equipment Acquired by IM-AGIMB
The equipment acquired by IM-AGIMB listed below was very useful in the research
activities in petroleum science performed by IMPA’s scientists, students, and visiting
collaborators.
backup tape device
HP Laser Jet 4100 DTN printer (double face)
imported equipment
•
•
•
•
2 Myrinet circuit plate (M3F-PCI64B-2)
Linecard (M3-SW16-8F)
long cable – 50 m (M3F-CB-50M)
5 Blank Front Panel (M3-BLANK)
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IM-AGIMB has been giving an important contribution to the expansion of the Brazilian
scientific collaboration with mathematicians from several countries in Latin America:
Argentina, Bolivia, Chile, Colombia, México, Peru, Uruguay e Venezuela. As planned in
the original project of IM-AGIMB, two kinds of actions have been conceived and are taking
place to consolidate and up-grade substantially the cooperation of Brazilian mathematics
with Latin America, as sketched below:
•
•
Tutorial missions at an introductory level, directed to young undergraduate students of
neighboring countries and advanced level tutorial missions, directed to advanced
undergraduate and graduate students, as well as researchers.
Visits of Latin American researchers to Brazil to collaborate with local mathematicians
in research projects and to participate in congresses, workshops and in Brazilian PostDoctoral programs.
As a consequence, the number of joint research works, visits and missions has increased
substantially, contributing to a general research environment in mathematics in the region.
Concerning introductory tutorial missions, particularly relevant were those done in Bolivia,
coordinated by A. Hefez of Fluminense Fed. University - UFF, promoting courses to
undergraduate students and subsequently inviting the best ones to pursue graduate
courses in UFF and other national institutions. Also, of great relevance, was the recent
promotion of IM-AGIMB and UMALCA of a School directed to undergraduate students
from Bolivia and neighboring countries, with courses in the areas of number theory,
dynamical systems and probability in mathematical economy.
Concerning tutorial missions of advanced level, special emphasis was given to the
presence of distinguished Brazilian mathematicians in the Instituto de Matematica y
Ciencias Afines - IMCA, particularly in the areas of optimization and computer graphics,
that IMCA wants to implement in Peru with the support from Brazil. Another important
mission is the First Regional Meeting in Probability and Mathematical Statistics to be held
in Buenos Aires, from September 30 – October 2, 2004, coordinated by A. Galves.
In another front, the multiple visits from Latin American researchers to national institutions
and their participation in local conferences was particularly successful in several research
areas such as dynamical systems, complex dynamics, probability, optimization, partial
differential equations, algebra and geometry, involving mathematicians from several
countries in the region, as mentioned above.
As a consequence, the number of joint research works, visits and scientific missions has
increased substantially, contributing to a global research environment in the region.
The specific activities were the following ones:
133
Tutorial missions at an introductory level
•
Visit of Sergio Xavier Mendonça to Bolivia to present an introductory course in
Differential Geometry, in the period of June 31 – July 31, 2002.
•
Invitation to Bolivian students to pursue Summer courses in the Fluminense Federal
Univ. from Jan. 6 – Feb. 28, 2003. They were selected in introductory tutorial courses
previously delivered in Bolivia by A. Hefez and S. Mendonça.
•
Participation of Abramo Hefez in the Bolivian Congress of Mathematicians, from
August 25-29, 2003. On this occation, the joint activities for the following year were
planned. He also gave a talk entitled “Diophantine equations from Fermat to Wiles”.
•
Tutorial mission of Rafael Ruggiero to Venezuela to deliver a mini-course “Geodeisc
Flows on surfaces” in the XVI Escola Venezuelana de Matematica, held in Merida from
September 7 – 13, 2003.
•
Another joint activity of UFF and IM-AGIMB was the invitation to 15 Latin American
students to take summer courses in early 2004, at Fluminense Fed. Univ. There were
5 students from Bolivia, 6 from Chile, 2 from Colombia and 2 from Peru.
•
IM-AGIMB and the Latin American and Caribbean Mathematical Union – UMALCA
organized a School from May 31 to June 12, 2004, in Cochabamba, directed to
undergraduate students from Bolivia and neighboring countries. Three courses were
offered: Number Theory, by C. Moreira, Dynamical Systems, by B. S.Martin and
Probability in Mathematical Economics, by L. Irineu , with the effective participation of
25 students, although many more informally attended the lectures.
Advanced Tutorial missions
•
Paulo Cezar P. Carvalho, Benar Svaiter, Claudia Sagastizabal, Luiz Velho, Mikhail
Solodov visited IMCA to deliver advanced courses on optimization and computer
graphics, in the period of October 6-17, 2003.
•
Hossein Movasati also visited IMCA to deliver a course in dynamical systems in the
period of April 9-25, 2003.
•
First Regional Meeting in Probability and Mathematical Statistics, Buenos Aires,
September 30-October, 2004.
Scientific Visits
•
Visit of Gonzalo Contreras, from CIMAT, Guanajuato, Mexico, from October 1-30,
2003, to the Federal University of Rio Grande do Sul to work with Artur Lopes and to
interact with Ph.D. students. Following that, he also visited the Federal University of
Minas Gerais to work with Mario Jorge Dias Carneiro, Sonia Pinto e Silvie Ollifson. In
both occasions, they developed research works in mechanics on Mather´s theory. In
the first case, Ruy Exel of the Fed. Univ. of Santa Catarina, was also involved.
•
Visit of Wilfredo Sosa, to IMPA in the period of March 10-April 10, 2003 to work with
the Optimization group (two recent articles in collaboration with A. Iusem: Iterative
algorithms for equilibrium problems. Optimization 52 (2003), 3, 301-316 and New
existence results for equilibrium problems. Nonlinear Anal. 52 (2003), 2, 621-635) and
with the Optimization group of LNCC (a recent article in collaboration with Fernanda
134
Raupp: A new approach to a multicriteria optimization problem. Numer. Algorithms 35
(2004), no. 2-4, 233-247)
•
Visit of Percy Fernandes to IMPA in the period of January 4-March 4, 2003, to
participate in the Post-Doctoral Summer Program and work in foliations with finite
automorphisms group in the projective space, with local complex dynamics
researchers.
•
Visit of Pedro Ubilla to UNICAMP, in the periods of June 1-18 and November 15-30,
2003 to work with D. Figueiredo, UNICAMP, J.P.Gossez, Univ. Libre de Bruselles,
J.M. Bezerra do Ó, Fed. Univ. of Paraiba and Ph.D. students. This visit lead to the
conclusion of research works. This collaboration also involves other mathematicians
from different institutions in Chile and Brazil. Djairo Figueiredo delivered the key
address at the meeting COMCA, 2004, in Chile.
•
Visit of Juan Tirao from Univ. Cordoba to IMPA, in the period of July 2003, to work with
J. Zubelli from IMPA, Alberto Grunbaum, UC, Berkeley and J.J. Duistermaat from
Utrecht.
•
Visit of Alicia Dickenstein to the University of São Paulo, São Carlos, in the period of
February 2-20, 2004, to deliver a minicourse “Discriminants, resultants and multidimensional discriminants” and a conference in a meeting organized by A. Hefez, at
the Fluminense Fed. University.
•
Visits of Mario Wschebor, Ricardo Fraiman e Ernesto Mordecki, from Uruguay, to work
with Pablo Ferrari and other probabilists from the University of São Paulo, under the
project “Networks, Trees, Complexity and Stochastic Matrices” in the periods of
October 19- 23, December 1-4, 2003 and January 26-30, 2004, respectively.
•
Visit of Roberto Markarian, from Uruguay, to IMPA in the period of November 15- 30,
2003, to work on “Ergodicity in billards with stochastic perturbations” with Vladas
Sidoravicius. The work is being concluded.
Participation in National Events
•
Participation of Latin American mathematicians in IMPA´s Pos-Docotoral Summer
program, in January and February 2003.
•
Participation of four mathematicians from Latin America in the Congress Complex
Analytic Methods In Dynamical Systems, held in IMPA in the period of August 25-29,
2003.
•
Participation of Uruguayan researchers and students in the XXIX Conference on
Stochastic Processes and their Applications - VII Brazilian School on Probability, Angra
dos Reis, August 3-9, 2003.
•
Moreover, there was an intense participation of Latin American researchers in the
many scientific events promoted by IM-AGIMB in all areas of mathematics that the
Institute comprises, according to the different reports.
135
Emerging Centers
A Brief Summary of the Reports
One of the fundamental tasks of IM-AGIMB is to support consolidating high level quality
research and teaching, especially at graduate level, in Emerging Centers in the Northern,
Northeastern and Central-West regions of Brazil.
The new concept presented here is that research groups in such Centers belong to the
same Virtual Institute of Excellence that comprises many of the more advanced groups in
the country. This provides a great stimulus to the Brazilian mathematical community as a
whole, in the sense of a global and integrated advancement as suggested by the very
name of the Institute.
The Emerging Centers have been able to plan their activities every year, or even for longer
periods, like for instance visits of researchers from national institutions or from abroad,
participation of their members in events and research activities in other national centers
and the acquisition of some books for their libraries and computational equipment. A fair
number of CNPq’s Scientific Initiation fellowhips have been provided to them via IMAGIMB.
At the beginning of the Institute’s activities, in January 2002, we had nine Emerging
Centers. Now we have twelve, and the last one in fact is a Virtual Emerging Center with
research groups from four different institutions. This gives an idea of the enthusiasm of
these IM-AGIMB groups from the Northern, Northeastern and Central-Western, together
with that of Federal University of Paraná, to be working together towards the advancement
of mathematics. A concrete result in this direction is that since the start of IM-AGIMB, four
Emerging Centers of them had their M.Sc. programs officially accredited by CAPES, the
Agency from the Ministry of Education that supervises the graduate programs in Brazil.
136
The Emerging Centers’ Reports of Activities will appear in the sequel, still in an
abbreviated format in this English version – the Portuguese version is slightly more
expanded. Here we just draw some conclusions from them. Most specially, it is quite clear
that the progress they all have experimented in the last two and half years, both in
research and nurturing of students, has been very impressive. Of course, more time and
continuation of efforts are needed to confirm the achievement. To a good extent, they
credit IM-AGIMB for such a globally organized successful drive for the Brazilian
Mathematics to reach a new and sustainable level of development across boundaries of
the different regions of the country.
In their Reports, the Emerging Centers stress the importance of their increasing
participation in the mathematical activities as a whole in Brazil. That includes not only the
possibility for their researchers to attend meetings and visit other centers, but reciprocally
they were able to have active researchers as visitors, as mentioned before. Going beyond
that, IM-AGIMB promoted Conferences/Workshops Schools in the Emerging Centers in
different subjects, formats and sometimes in partnership with other groups/institutions. In
this respect, we can mention several meetings in the Emerging Centers of Amazonas,
Alagoas, Bahia, Pará, jointly Paraíba and Campina Grande, and Paraná.
It is important to point out that good level research is increasingly taking place at the
Centers, resulting in a fair number of publications in reputable mathematical journals. New
hiring of young mathematicians are taking place, the best candidates being Ph.Ds. from
our main institutions in Brazil or abroad.
On the nurturing of students, there is much priority in two fronts. The first one is through
the Scientific Initiation fellowships granted to the best undergraduate students. In the
second front, there has been an upgrading of M.Sc. programs: The Centers from
Amazonas, Alagoas, Pará and Paraná had their M.Sc. programs officially recognized by
CAPES since the start of IM-AGIMB, joining the ones in Bahia, Paraíba – João Pessoa
and Goiás. This is quite a remarkable event and a very stimulating one to other Centers!
137
Report
Emerging Center
Federal University of Alagoas
Coordinator: H. Alencar
Impact of the IM-AGIMB
Since 2002, we have been able to plan in an effective way our activities in scientific
exchanges, graduate work, research, scientific initiation, teacher training and acquisition of
books and computer equipment. In 2004 our M.Sc. program, accredited by CAPES, was
launched.
Scientific Initiation and M.Sc. Program
In 2001, we had only 4 students. Now we have 16 fellows with the help of AGIMB, and in
our experience, they get a faster and better formation, allowing them to enter graduate
programs without difficulties. We are sure that most of them will intend to return to our
state, due to the better working conditions we expect to be able to offer. In the first group
of 5 students in the M.Sc. program, 3 were former IC students, and have been also
accepted in graduate programs with grade 6,7 in Capes evaluation.
High School Teachers Training
In 2002, it was held for the first time in Alagoas, a workshop via Videoconferences
promoted by IM-AGIMB. Besides the obvious educational importance, this event implied
that UFAL internet is now connected to RNP.
Research and Mobility
The increase in productivity was remarkable. Several articles were published in
international journals and several of our faculty members gave talks in national and
international meetings. Visits of researchers from other centers to UFAL and a planned
exchange of our faculty became possible.
Events
In January 2004 we held, with the help of AGIMB, a workshop in Chaotic Dynamics and
Submanifold Geometry, with the participation of most of the main national researchers and
several foreign visitors.
138
Research areas: Analysis, Differential Geometry, Dynamical Systems
1. Hilário Alencar, H. Rosenberg and W. Santos, On the Gauss Map of Hypersurfaces
with Constant Scalar Curvature in Spheres, Proceedings of the American
Mathematical Society, 2004.
2. Adán Corcho, Ill Posedness for the Benney System. Discrete and Continuous
Dynamical Systems, 2004.
3. Adán Corcho and Felipe Linares, Well-Posedness for the Schrödinger-Debye
Equation, Contemporary Mathematics, 2004.
4. Arbieto, C. Matheus e K. Oliveira, Equilibrium states for random non-uniformly
expanding maps, Nonlinearity, 17, 581-593, 2004.
5. J.F. Alves, K. Oliveira and A. Tahzibi, Continuity of SRB Entropy for Endomorphisms.
Proceedings of Equadiff 2003, resumo extendido, 2004.
6. F. Mercuri and Adonai Seixas, Hypersuperfaces of cohomogeneity one and
hypersarfaces of revolution. Differential Geometry and its Applications, 20, 225-239,
2004.
7. Arbieto, C. Matheus and K. Oliveira. O trabalho de Ennio De Giorgi sobre o problema
de Plateau. Revista Matemática Universitária, 35, 1-29, 2003.
8. Krerley Oliveira, Equilibrium states for non-uniformly expanding maps. Ergodic Theory
and Dynamical Systems, 23, 1891-1906, 2003.
9. Hilário Alencar, M. do Carmo and M.F. Elbert, Stability of Hypersurfaces with
Vanishing r-Mean Curvatures in Euclidean Spaces, Journal fur Die Reine und
Angewandte Mathematik, 554, 201-216, 2003.
10. Hilário Alencar, M. do Carmo and W. Santos. A Gap Theorem for Hypersurfaces of
the Sphere with Constant Scalar Curvature One, Commentarri Mathematici Helvetici,
77, 549-562, 2002.
Submitted
1. C. Matheus and K. Oliveira, Geometrical versus topological properties of Manifolds.
Submitted to Journal of Institute of Mathematics of Jussieu.
2. J.F. Alves, K. Oliveira, A. Tahzibi, Continuity of Entropy for Endomorphisms.
Submitted to Communications of Mathematical Physics.
Books
1. Geometria das Curvas Planas. Página Inicial: 1. Pages 255. Rio de Janeiro. Edited by
IMPA, 2003. Colaboration with Walcy Santos
139
Report
Emerging Center
Federal University of Amazonas
Coordinator: R. Tribuzy
Impact of the IM-AGIMB
Since 2002 we have been able to plan and execute activities with enthusiasm. IM-AGIMB
has helped us with library resources, travel and Scientific Initiation fellowships. This was
instrumental for the recommendation by CAPES to our M.Sc. program, which allowed us
to train 12 M.Sc. students. All of them are doing their Ph.D.s in institutions recommended
by CAPES and we expect that most of them will become futurely faculty members. The
Institute also promoted mobility of research mathematicians.
Mobility
Besides enhancing our program to receive visiting professors, our researchers were able
to participated in scientific meetings such as Escolas de Geometria XII e XIII, XXIV
Colóquio Brasileiro de Matemática and Seminário de Geometria Diferencial in honor of
João Lucas Barbosa. IM-AGIMB promoted an extended visit of faculty member J.K.
Martins to the Universidade Federal do Ceará.
Scientific Initiation
With the support of IM-AGIMB, we have obtained more fellowships and, as consequence,
also from CNPq’s PIBIC program, in which we now have a much more effective leverage.
Research Areas
Geometry of Submanifolds, Image Processing
1. Martins, José Kenedy. Hopf Hypersurfaces in space forms. Boletim da Sociedade
Brasileira de Matemática, Brasil, 35, 2004.
2. Mota, C., Dorr, M., Stuke, I., Barth, E. Categorization of transparent-motion patterns
using the projective plane. International Journal of Computer Information Science, 5(2),
119-140, 2004.
3. Stuke, I., Aach, T., Barth, E., Mota, C. Multiple-motion estimation by block-matching
using Markov random fields. International Journal of Computer Information Science.
5(2), 141-152, 2004.
4. Stuke, I., Aach, T., Barth, E., Mota, C. Analysing superimposed oriented patterns. In:
IEEE Southwest Symposium on Image Analysis, 2004, Lake Tahoe, NV, to appear,
133-137, 2004.
5. Mota, C., Dorr, M., Stuke, I., Barth, E. Analysis and synthesis of motion patterns using
the projective plane In: ISandT SPIE 16th Annual Symposium on Electronic Imaging
Science and Technology, 2004, San Jose, CA. Proceedings of SPIE: Human Vision
and Electronic Imaging IX, 5292, 174-181, 2004.
140
6. Aach, T., Stuke, I., Mota, C., Barth, E. Estimation of multiple local orientations in image
signals. In: IEEE International Conference on Acoustics, Speech, and Signal
Processing, Quebec, 2004.
7. Stuke, I., Aach, T., Barth, E., Mota, C. Estimation of multiple motions using block
matching and Markov random fields. In: ISandT SPIE 16th Annual Symposium on
Electronic Imaging Science and Technology, 2004, San Jose, CA. Proceedings of
SPIE: Visual Communications and Image Processing 2004, 5308, 486-496, 2004.
8. Mota, C., Stuke, I., Aach, T., Barth, E. Estimation of multiple orientations at corners
and junctions. In: 6th Pattern Recognition Symposium (DAGM'04), Tübingen, 2004.
9. Mota, C., Aach, T., Stuke, I., Barth, E. Estimation of multiple orientations in multidimensional signals In: IEEE International Conference on Image Processing,
Cingapura, 2004.
10. Haker, M., Mota, C., Barth, E. Multiple Motions in the Projective Plane. In: 7th
Tübingen Perception Conference, 2004. Kirchentellinsfurt: Knirsch Verlag, 177-177,
2004.
11. Mota, C., Dorr, M., Stuke, I., Barth, E. Categorization of transparent-motion patterns
using the projective plane In: Fourth International Conference on Software
Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing,
2003, Lübeck. Mt.Pleasant, MI: ACIS, 363-369, 2003.
12. Stuke, I., Aach, T., Mota, C., Barth, E. Estimation of Multiple Motions: Regularization
and Performance Evaluation In: ISandT SPIE 15th Annual Symposium on Electronic
Imaging, Santa Clara, 5022, 2003.
13. Stuke, I., Aach, T., Barth, E., Mota, C. Estimation of multiple motions by block matching
In: Fourth International Conference on Software Engineering, Artificial Intelligence,
Networking and Parallel/Distributed Computing (SNPD'03), 2003, Lübeck. Mt.Pleasant,
MI: ACIS, 358-362, 2003.
14. Stuke, I., Aach, T., Mota, C., Barth, E. Linear and regularized solutions for multiple
motions In: IEEE International Conference on Acoustics, Speech, and Signal
Processing, Hong Kong. Proc. of ICASSP 2003, 1, 2003.
15. Barth, E., Stuke, I., Aach, T., Mota, C. Spatio-temporal motion estimation for
transparency and occlusion In: IEEE International Conference on Image Processing,
2003, Barcelona. Proc. of ICIP, IEEE Press, 1, 2003.
16. Haker, M., Mota, C. Softwares sem registro ou patente: PPMotion: a tool for synthesis
of transparent motion, 2003
17. Tribuzy, R. A., Eschenburg, J., Ferreira, M., Burstall, F. Kähler Submanifold with
Parallel Pluri-mean Curvature. Differential Geometry and its Applications, 2003.
18. Tribuzy, R. A., Ferreira, M. Codimension Two Kähler Submanifolds of Space Forms.
Archiv der Mathematik. Alemanha, 79, 520-528, 2002.
19. Barth, E., Stuke, I., Mota, C. Analysis of motion and curvature in image sequences In:
Fifth IEEE Southwest Symposium on Image Analysis and Interpretation, Santa Fe.
Proceedings SSIAI 2002. IEEE Computer Press, 1, 206-210, 2002.
141
Report
Emerging Center
Federal University of Bahia
Coordinator: Enaldo da Silva Vergasta
Ours is the only Federal University in our state, and the only University of a bigger size.
We offer a B.Sc. and a M.Sc. program in Mathematics.
Infrastructure and Library
Computer equipments were added to the student computer labs, spatially to our teaching
laboratory. We have purchased books in the areas of Differential Geometry, Dynamical
Systems, Algebra and Optimization. In our University, in particular, the latter were almost
nonexistent, so our acquisitions have been instrumental to help establishing this area.
Mobility
We emphasize interactions with researchers Federal University of Ceará - UFC
(Differential Geometry and Dynamical Systems), University of São Paulo - USP
(Dynamical Systems) and State University of São Paulo UNESP/SJRP (Algebra).
Internationally, with the Dynamical Systems group University of Porto. AGIMB resources
were important to allow participation of our faculty in events such as School of Differential
Geometry at Federal University of Goiás, International Workshop on Robustness and
Partial Hyperbolicity, Búzios, and 24o Colóquio Brasileiro de Matemática at IMPA.
High School Teachers Training
Since January 2003, UFBA participates at the High School Teachers Training promoted by
IM-AGIMB in partnership IMPA and RNP. In the four workshops (January and July 2003,
2004), an average of 80 teachers have participated.
AGIMB has grantes us 10 scientific initiation scholarships which has been devoted to
studies in Differential Geometry, Analysis, Algebra and Optimization; the latter is an
emerging area. Some of the fellows are going to start their M.Sc. in arch 2005
Events
In October 2004 we will host II Bienal da Sociedade Brasileira de Matemática with 1.500
participants from the whole country. IM-AGIMB is helping to promote and fund this event.
142
For details on research lines and scientific production, see the detailed report
Commutative algebra
Carlos Eduardo Nogueira Bahiano
Noncommutative algebra, discrete mathematics, combinatorics
Thierry Corrêa Petit Lobão
Stochastic Differential Equations
Edson Alberto Coayla Teran
Enaldo Silva Vergasta
Ézio de Araújo Costa
Isaac Costa Lázaro
José Nelson Bastos Barbosa
Marco Antonio Nogueira Fernandes
Rita de Cássia de Jesus Silva
Optimization
Isamara Carvalho Alves
Dynamical Systems
Augusto Armando de Castro Júnior
Vilton Jeovan Viana Pinheiro
Publication
§
Commutative algebra
Bahiano, C.E.N., Symbolic powers of edge ideals, Journal of Algebra, 273(2), 517-537,
2004.
§
Noncommutative algebra
Petit Lobão, Thierry, Sehgal, Sudarshan. K., The normalizer property for integral group
rings of complete monomial groups, Communications in Algebra, 31(6), 2971-2983, 2003.
Petit Lobão, Thierry, Polcino Milies,,The normalizer property for integral group rings of
Frobenius groups, Journal of Algebra, 256(1), 1-6, 2002
§
Stochastic Differential Equations
Coayla-Teran, E.A., Ruffino, P., Stochastics Versions of Hartman-Grobman Theorems,
Stochastics and Dynamics, 4(4), 1-23, 2004.
Coayla-Teran, E.A., Magalhaes, P.M.D., Weak Solutions for Stochastic FitzHugh-Nagumo
Equations, Stochastic Analysis and Applications, 21(2), 443-463, 2003.
143
§
Barbosa, J.N., Hypersurfaces of Sn+1 with two distinct principal curvatures. Glasgow J. of
Math., 2004.
Barbosa, J.N., Isospectral hypersurfaces of Sn+1, Kodai Math. J., 2004.
Costa, Ézio de Araújo, On Einstein four-manifolds, Journal of Geometry and Physics, 51,
244-255, 2004.
Barbosa, J.N., Barros, A., A lower bound for the norm of the second fundamental form of
minimal hypersurfaces of Sn+1, Archiv der Mathematik, Basel, 81(4), 478-484, 2003.
Barbosa, J.N., Brasil JR, Aldir, Costa, Ézio de Araújo, Lázaro, Isaac Costa,
Hypersurfaces of the Euclidean sphere with nonnegative Ricci curvature, Archiv der
Mathematik Basel, 81(3), 335-341, 2003.
Fernandes, M.A.N., Martin, Luiz Antonio Barrera San Geometric proprieties of invariant
connections on SL(n,R)/SO(n), Journal of Geometry and Physics, 47, 369-377, 2003.
§
Discrete Mathematics, Combinatorics
Petit Lobão, Thierry, Pinho, S. T. R., Rigorous Results of Aperiodic and Almost Periodic
Sequences, Brazilian Journal of Physics, 30(4), 772-777, 2000.
§
Dynamical Systems
Alves, José F., Castro Junior, Augusto Armando de, Pinheiro, V.J.V., Backward volume
contraction for endomorphisms with eventual volume expansion, Comptes Rendus de
LÁcademie des Sciences Serie I-Mathematique, 2004.
Alves, José F., Luzzatto, Stefano, Pinheiro, V. J. V., Lyapunov exponents and rates of
mixing for one-dimensional maps, Ergodic Theory And Dynamical Systems, 24, 1-22,
2004.
Alves, José F., Luzzatto, Stefano, Pinheiro, V. J. V., Markov structures and decay of
correlations for non-uniformly expanding dynamical systems, Annales de LÍnstitut Henri
Poincaré-Analyse Non Linéaire, 2004.
Castro Junior, A. A., Fast Mixing for partially hyperbolic attractors with mostly contracting
central direction, Ergodic Theory and Dynamical Systems, 24(1), 17-44, 2004.
Castro Junior, A. A., Medida e Integração. 150 páginas. Livro aceito para publicação no
Projeto Euclides, IMPA, Rio de Janeiro, 2004.
Alves, José F., Luzzatto, Stefano, Pinheiro, V. J. V., Markov structures for non-uniformly
expanding maps on compact manifolds in arbitrary dimension. Electronic Reseach
Announcement of Amer. Math. Soc., 9, 26-31, 2003.
Colli, E., Pinheiro, V.J.V., Chaos versus renormalization at quadratic S-unimodal
Misiurewicz bifurcations, Astérisque, 286, 257-308, 2003.
Castro Junior, A. A., Backward inducing and exponential decay of correlations for partially
hyperbolic attractors, Israel Journal of Mathematics, 130, 2002.
144
Report
Emerging Center
Federal University of Campina Grande
Coordinator: Aparecido Jesuíno de Souza
Impact of IM in the working conditions, research and graduate program
AGIMB contributed substantially to enhancing the working conditions, in terms of computer
equipment and library, and allowing the effective planning of new activities. Our faculty
now has 5 computers, and with the renewed motivation towards research and more
contact with other centers, our best expectations were totally fulfilled. We should say that
until 2002, we merely taught classes, mainly to other Departments, and there was no
investment on more advanced books
Mobility
With the help of AGIMB we consolidated the exchanges with other mathematical centers
of the country, through joint research projects and work with researchers from IMPA,
UNICAMP, UFPA, UFV, USP-São Carlos, UFMG, UFU, UFPB, UFPE, and foreign
institutions.
Events
With the help of AGIMB, we hosted in January 2004 a joint Workshop with UFPB in honor
of the 70th birthday of Prof. Djairo Figueiredo with the participation of 25 researchers from
Brazil and abroad. We have also promoted Elementary and High School Olympiads in
Campina Grande and nearby towns, with more than e 2000 candidates in the most recent
edition, May 2004.
Scientific Initiation and Graduate program
With the help of AGIMB we are now certain that our best undergraduate students will have
support, and our new M.Sc, program had a enthusiastic start.
Areas of Research (For publications, see the detailed report)
•
•
•
•
•
•
•
Hamiltonian systems
Elliptic and Hyperbolic PDEs
Evolution PDEs
Bayesian Inference
Conservation laws
Fluid dynamics
Matroids
145
1. Doronin, G. G., Lar'kin, N. A., Souza, A. J., Existence and stability of global regular
solutions for a dusty gas model, Mathematical Methods in the Applied Sciences,
Alemanha, 27(4), 441-456, 2004.
2. Alves, C. O., Morais Filho, D. C., Miyagaki, O. H., Multiple solutions for an elliptic
system on bounded and unbounded domains, Journal of Nonlinear Analysis, USA,
56(4), 555-568, 2004.
3. Alves, C. O., Ó, J. M. B., Miyagaki, O. H., On nonlinear perturbations of a periodic
elliptic problem in R2 involving critical growth, Journal of Nonlinear Analysis, USA,
56(5), 781-791, 2004.
4. Galiscan, E., Bounded Holomorphic Mappings and the Compact Approximation
Property in Banach Spaces, Journal Portugaliae Mathematica, 61(1), 2004.
5. Alves, C. O., Bertone, A. M., A discontinuous problem involving the p-Laplacian
operator and critical exponent in RN, Electron J. Differential Equations, USA, 42, 1-10,
2003.
6. Alves, C. O., Carrião, P. C., Miyagaki, O. H., Existence of homoclinic orbits for
asymptotically periodic systems involving Duffing like equation, Applied Mathematics
Letters, 16, 639-642, 2003.
7. Alves, C. O., Y. H. Ding, Multiplicity of Positive solutions to a p-Laplacian equation
involving critical nonlinearity, Journal of Mathematical Analysis and Applications, 508521, 2003.
8. Alves, C. O., Carrião, P. C., Miyagaki, O. H., Nontrivial solutions of a class of
quasilinear elliptic problems involving critical exponents, Progress in Nonlinear
Differential Equations and their applications, Alemanha, 54, 225-238, 2003.
9. Alves, C. O., Miyagaki, O. H., Ó, J. M. B., On a class of singular Biharmonic problems
involving critical exponents. Journal of Mathematical Analysis and Applications,
Estados Unidos, 12-26, 2003.
10. Alves, C. O., Soares, S. H. M., J. Yang, On the existence and concentration of
solutions for a class of Hamiltonian systems in RN, Advanced Nonlinear Studies, 3,
161-180, 2003.
11. Doronin, G. G., Lar'kin, N. A., Souza, A. J. Global Solutions for a Dusty Media Model.
Hyperbolic Problems Theory Numerics Applications, T.Y.Hou-E.Tadmor Eds, New
York, Estados Unidos, 519-528, 2003.
12. Pellegrino, D. M., Strongly almost summing holomorphic mappings. J. Math. Anal.
Appl. 287 (1), 246-254, 2003.
13. Pellegrino, D. M., Cotype and absolutely summing homogeneous polynomials in Lp
Spaces. Studia Mathematica, 157(2), 121-131, 2003.
14. Souza, A. J., Mota, J. C., Marchesin, D., Teixeira, P. W., A Simplified Oxidation Model
for Two-Phase Flow in porous Media. RETERM - Revista de Engenharia Térmica,
Brasil, 2, 9-14, 2002.
15. Mota, J. C.; Souza, A. J.; Garcia, R. A. and Teixeira, P. W., Oxidation Fronts in a
Simplified Model for Two-Phase Flow in Porous Media, MATEMÁTICA
CONTEMPORÊNEA, Brasil, 22, 67-82, 2002. ISSN 0103-9059.
146
16. Doronin, G. G. and Lar´Kin, N. A. Kumamoto-Sivashinsky Approximation for the TwoPhase Flow of a Dusty Gas, Matemática Contemporênea, Brasil, 22, 83-95, 2002.
INSS 0103-9059.
17. Junior, B.M., Connected matroid with a small circumference. Discrete Mathematics, 25,
47-161, 2002. ISSN 0012-365X
18. SOUTO, M. A. S., On the Location of the Peaks of Least-Energy Solutions to
Semilinear Dirichlet Problems with Critical Growth, Abstract and Applied Analyses,
7(10), 547-561, 2002. ISSN 1085-3375.
19. Alves, C. O. and Souto, M. A. S., On Existence and Concentration Behavior of Ground
State Solutions for a Class of Problems with Critical Growth, Communication on Pure
and Applied Analyses, 1(3), 133-147, 2002. ISSN 1534-0392.
20. Souza, A. J.; Mota, J. C.; Marchesin, D. and Teixeira, P. W., A Simplifield Oxidation
Model for Two-Phase Flow in porous Media, RETERM, Revista de Engenharia
Térmica, Brasil, 2, 9-12, 2002.
21. Melo, A. L. and Gonçalves, J. V. A., Multiple sign changing solutions in a class of
Quasilinear Equations. Differential and Integral Equations, 15(2), 147-165, 2002.
22. De Souza, F. A. M. and Paula, G. A., Deviance Residuals for an Angular Response,
Aust. N. Z. J. Stat., 44(2 or 3), 901-999, 2002.
147
Report
Emerging Center
Federal University of Espírito Santo
Coordinator: Florêncio Guimarães Filho and Valmecir dos Santos Bayer
Impact of IM-AGIMB
IM-AGIMB has helped us with an extra quota of IC fellowships and is giving support to our
plans to obtain accreditation of a M.Sc. program. See the detailed report on the IC
activities. In terms of infrastructure, we have purchased four Pentium 4 computer and a
Laser HP 1200 printer. We have purchased many books in a planned way. We have
obtained authorization and hired 9 new faculty members. Several of our faculty have
participated in meetings.
Teacher Training
Since 2002 we participate in the Videoconference courses given by Elon Lages Lima,
Eduardo Wagner, Paulo Cezar Carvalho and Augusto César Morgado. 307 teachers from
the capital and from the interior have participated.
Research Areas
1. Algebra and Algebraic Geometry
Dra. Ana Claudia Locateli (Doctor – IME/USP)
Dr. José Gilvan de Oliveira (Doctor - IMPA)
Dra. Regina Maria de Aquino (Doctor – IME/USP)
Dr. Valmecir Antônio dos Santos Bayer (Doctor - IMPA)
2. Analysis and PDEs
Dr. Domingos Sávio Valério Silva (Doctor - IMPA)
Dr. José Armínio Ferreira (Doctor – IM/UFRJ)
Dra. Liane Bordignon (Doctor – IME/USP)
Dr. Luiz Fernando Cassiani Camargo (Doctor - UNICAMP)
Dr. Joccitiel Dias da Silva (Doctor – IM/UFRJ)
3. Differential Geometry
Dr. Florêncio Ferreira Guimarães Filho (Doctor - IMPA)
Dr. Elias Marion Guio (Doctor – PUC/RJ) - Bolsista CNPq
Dr. José Miguel Malacarne (Doctor - UFC)
148
4. Dynamical Systems
Dr. Magno Branco Alves (Doctor – PUC/RJ)
Dr. Milton Edwin Cobo Cortez (Doctor - IMPA)
5. Matrix Analysis and Optimization
Dr. Humberto José Bortolossi (Doctor – PUC/RJ)
Dr. Ricardo Soares Leite (Doctor – PUC/RJ)
1. Alías, L.J., Malacarne, J.M., On the first eigenvalue of the linearized operator of the
higher order mean curvature for closed hypersurfaces in space forms. Illinois Journal of
Mathematics, 48(1), 219-240, 2004.
2. Silva, E.A.B., Xavier, M.S., Multiplicity of solutions for quasilinear elliptic systems with
critical growth, Nonlinear Differential Equation Appl., 2004.
3. Munaro, C.J., Rosado Filho, M., Munareto, S.S., Control of feedback linearizable
uncertain nonlinear systems using a parameter identifier, 2004, Gramado (RS) Brasil.
Anais do XV Congresso Brasileiro de Automática, 2004.
4. Barrientos, A.M., Some results about a bidimensional version of the generalized BO.
Communications on Pure and Apllied Analysis, 2(2), 233-249, 2003.
5. E.A.B. Silva, M.S. Xavier, Multiplicity of solutions for quasilinear elliptic problems
involving critical Sobolev exponents, Ann. Inst. H.Poincaré, Analyse Non Linéaire
20(2), p.341-358, 2003.
6. Leite, R.S., Tomei, C., Parameterization by polytopes of intersections of orbits by
conjugation. Linear Algebra and its Applications, 361, 223-243, 2003.
7. Alías, L.J., Malacarne, J.M. Spacelike hypersurfaces with constant higher order mean
curvature in the Minkowski space-time. Journal of Geometry and Physics, 41(4), 359375, 2002.
8. Aledo, J.A., Alías, L.J., Malacarne, J.M., Pastor, J.A., Appendix to ‘Spacelike
hypersurfaces with constant higher order mean curvature in the Minkowski space-time’.
Journal of Geometry and Physics, 41(4), 376-379, 2002.
9. Alías, L.J., Malacarne, J.M., Constant scalar curvature hypersurfaces with spherical
boundary in Euclidean space. Revista Matemática Iberoamericana. Madri, Espanha,
18(2), 431-442, 2002.
10. Alías, L.J., Malacarne, J.M., Hypersurfaces with constant higher order mean curvature
in
Euclidean
space
In:
Differential
Geometry,
2001,
Valencia.
Proceedings of the International Conference held to honour the 60th Birthday of A M
Naveira Editors O Gil-Medrano, V Miquel. Singapore: World Scientific Publishing Co.
Pte. Ltd., 28-58, 2002.
11. Cortez, Milton Edwin Cobo, Gutierrez, Carlos, Llibre, Jaume, On the injectivity of C1maps of the real plane. Canadian Journal of Mathematics. Inglaterra, 54(6), 11871201, 2002.
149
12. Cortez, Milton Edwin Cobo. Piece-wise affine maps conjugate to interval exchanges.
Ergodic Theory and Dynamical Systems. Reino Unido, 22, 375-407, 2002.
13. Munaro, Celso José, Rosado Filho, M., Borges, R. M., Munareto, S. S., Costa, W.T.,
Ambiente integrado para controle e estimação em sistemas não lineares via técnica da
linearização exata. In: XIV Congresso Brasileiro de Automática, 2002, Natal. Anais do
XIV Congresso Brasileiro de Automática, 1428-1433, 2002
14. Munaro, Celso José, Rosado Filho, M., Borges, R. M., Munareto, S.S., Costa, W.T.,
Modeling and observer-based nonlinear control of a magnetic levitation system In:
2002 IEEE Joint International Conference on Control Applications and International
Symposium on Intelligent Control, 2002, Glasgow, Proceedings of the 2002 IEEE
International Conference on Control Applications, 162-167, 2002.
15. Munaro, Celso José, Rosado Filho, M., Borges, R.M., Munareto, S.S., Costa, W.T.,
Nonlinear tracking control design for magnetic levitation system In: XIV Congresso
Brasileiro de Automática, 2002, Natal, Anais do XIV Congresso Brasileiro de
Automática, 2178-2183, 2002.
Observer-based nonlinear control application of a magnetic levitation system In: V
Conferência de Aplicações Industriais, 2002, Salvador, Proceedings of the V IEEE
Industry Applications Conference, 2002.
Stabilizing control design of fully linearizable systems via estimated states In: 2002
IEEE Joint International Conference on Control Applications and International
Symposium on Intelligent Control, 2002, Glasgow, Proceedings of the 2002 IEEE
International Conference on Control Applications, 1333-1338, 2002.
150
Relatório
Centro em Desenvolvimento
Universidade Federal de Goiás
Coordenador: Ronaldo Garcia
Mobilização
Este instituto virtual poderá vir a ser uma importante contribuição na consolidação da
pesquisa em centros emergentes no interior do Brasil. Em particular o IME/UFG tem feito
nos últimos anos um trabalho de base (formação de discentes, coordenação de cursos no
interior do Estado, qualificação do seu quadro docente – doutorado e pós-doutorado). O
aporte de recursos financeiros para o intercâmbio acadêmico será fundamental para
daruma perspectiva aos recém doutores do IME.
Cursos de Aperfeiçoamento
Através do IM-AGIMB estão sendo realizados cursos de aperfeiçoamento de professores
do ensino fundamental e médio com uso da tecnologia (internet) e presença de
professores nos centros em desenvolvimento. Já foram realizadas 5 cursos de
aperfeiçoamento com a participação do IME/UFG. A demanda para o curso é crescente.
Os dados completos de participação em cada etapa foram encaminhados aos
coordenadores do curso no IMPA.
Iniciação Científica
O IM-AGIMB está sendo uma importante fonte de recursos para incremento na formação
de bacharéis no curso de matemática da UFG. Em 2004 temos 10 bolsistas de Iniciação
Científica (cota do IM-AGIMB) que, quando concluírem a graduação terão plena
capacidade de cursar o mestrado em outros centros. Além das bolsas de IC do Milênio
em 2004 conseguimos no programa PIBIC/UFG-CNPq mais 10 bolsas de IC em 2004.
Acreditamos que as bolsas de IC do Milênio foram de fundamental importância para o
incremento das bolsas de IC do programa PIBIC no Instituto. Os atuais alunos bolsistas
deverão cursar o mestrado em outros centros (IMPA, USP, UnB), atingindo uma prática
docente do IME em incentivar a integração com outros centros.
Pós-Graduação
O mestrado de matemática do IME/UFG foi criado em 1973 e somente a partir de 1996
passou a receber bolsas da CAPES. Atualmente temos 25 alunos regulares, originários
da graduação de matemática da UFG e de outros centros. Do total de alunos regulares
temos 11 bolsistas (CAPES, CNPq e UFG). A execução do projeto IM - AGIMB poderá vir
a refletir positivamente nos indicadores do curso pela possibilidade de intercâmbio entre
pesquisadores e direcionando os mestres formados no IME a cursarem o doutorado em
centros consolidados. Vários mestres formados no IME que foram bolsistas de IC no IME,
programa PIBIC, estão atualmente cursando doutorado (IMPA, UnB e UNICAMP). Esta
meta com certeza se repetirá com os atuais bolsistas de IC do IM-AGIMB. Atualmente o
curso de mestrado de matemática da UFG tem conceito 4 na CAPES.
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Eventos
O IME/UFG realiza anualmente, desde 1986, um encontro de matemática e estatística
com atividades voltadas principalmente para os alunos de graduação e mestrado. São
oferecidos minicursos, conferências plenárias, sessões especiais, posters, etc. Em média
temos 400 participantes inscritos por evento. Em 2004 a previsão é realizar este evento
no mês de outubro.
No período de execução do projeto IM-AGIMB/IMPA-OS os seguintes eventos foram
realizados no IME.
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Curso de aperfeiçoamento de professores: julho/2002, janeiro/2003, julho/2003,
janeiro/2004 e julho/2004.
Encontro de Matemática e Estatística: setembro/2002, junho/2003 e outubro/2004.
Olimpíada de Matemática de Goiás: outubro/2002, outubro/2003 e setembro/2004.
Escolas de verão: 2002, 2003 e 2004.
XII Escola de Geometria: julho/2002.
Sobre os eventos realizados pelo IME temos clareza do alcance dos seus objetivos. Por
exemplo, na XII Escola de Geometria de 2002, realizada em Goiânia, do total de
aproximadamente 350 participantes, aproximadamente 120 alunos de graduação da UFG
participaram do evento e neste ano 15 alunos do curso de bacharelado de matemática da
UFG participaram da Escola na USP.
Os encontros de matemática e estatística realizados pelo IME/UFG tem contado sempre
com conferencistas renomados do Brasil e do exterior.
Publicações
O IME/UFG publica anualmente a Revista da Olimpíada de Matemática do Estado de
Goiás. Em 2004 será publicado o volume 05. Os 04 livros editados para a XII Escola de
Geometria estão indexados no Math. Review e Zentralblatt. Os mesmos foram doados
para boa parte das bibliotecas das universidades federais e estaduais do Brasil e para a
biblioteca do IMPA.
Contribuição do IM-AGIMB
A contribuição do IM-AGIMB ao IME/UFG (centro em desenvolvimento) é marcada pela
melhoria da infra-estrutura do Instituto para suas atividades de ensino e pesquisa. Em
especial destacamos:
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Aquisição de computadores destinados às atividades fins de formação de recursos
humanos;
Aquisição de livros que estão sendo incorporados ao acervo da Biblioteca Central da
UFG, melhorando e atualizando seu acervo com publicações recentes;
Outra contribuição importante do IM-AGIMB refere-se aos recursos de custeio para:
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Realização de intercâmbio acadêmico (visitas de curta duração);
Realização de eventos no âmbito do Instituto e dos campi da UFG;
Compra de material de consumo, complemento importante no orçamento do IME.
Finalmente destacamos a realização de cursos de aperfeiçoamento de professores tendo
participação integrada do IMPA com vários centros localizados em todas as regiões
geográficas do Brasil, incluindo o IME/UFG.
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Impacto do IM-AGIMB
A execução do projeto trouxe até o presente os seguintes impactos positivos nas
atividades docentes no IME/UFG.
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Incremento e consolidação de intecâmbio acadêmico com pesquisadores de centros
consolidados e emergentes;
Intercâmbio acadêmico com pesquisadores de centros no exterior (Espanha, Chile,
França, Estados Unidos);
Incremento na produção científica do quadro docente do curso de mestrado de
matemática;
Incremento substancial no número de bolsas de Iniciação Científica, com avaliação
positiva dos resultados obtidos com este investimento. Os bolsistas de IC deverão
cursar mestrado/doutorado em centros reconhecidos pela CAPES;
Qualificação do quadro docente do Instituto de Matemática (atualmente temos 23
doutores em matemática, outros 06 estão cursando doutorado e 05 fizeram estágio de
pós-doutorado nos últimos 02 anos);
Realização de eventos de âmbito nacional e internacional promovendo a matemática
desde o ensino fundamental e médio (olimpíadas), graduação, e pós-graduação.
Desenvolvimento de pesquisa em colaboração com pesquisadores de centros
consolidados (IMPA, USP S. Paulo, USP S. Carlos, UNICAMP, UnB, UFRJ) e centros
em desenvolvimento (UFPI, UNESP, UFCG).
Consolidação das atividades de pesquisa nas diversas áreas de atuação do quadro
docente do IME (álgebra, análise, geometria, otimização e sistemas dinâmicos).
Recursos
O IM-AGIMB disponibiliza aos centros em desenvolvimento recursos de custeio
(passagens, diárias e serviços) e capital (livros e computadores). Este aporte de tem sido
um complemento importante para melhorar as condições de ensino e pesquisa no IME.
Os computadores adquiridos estão disponibilizados aos alunos de graduação e mestrado
nos laboratórios do IME. Os livros foram encaminhados a Biblioteca Central da UFG onde
toda a comunidade tem acesso de uso dos mesmos. Foram adquiridos, com o recurso de
R$14.000,00 (quatorze mil reais), aproximadamente 120 títulos. Estamos na fase final da
compra dos livros.
Intercâmbio
Os recursos do IM-AGIMB tem sido usados no IME/UFG na concessão de auxílio para
viagens de curta duração de professores do Instituto e para receber pesquisadores no
âmbito do IME, especialmente nos eventos realizados pelo Instituto, incluindo seminários.
Nota-se nitidamente no IME o intercâmbio docente com pesquisadores de vários centros
brasileiros consolidados e emergentes. Citamos os intercâmbios com os seguintes
centros nacionais: IMPA, UnB, USP-S. Paulo, USP-S. Carlos, UNICAMP, UFC, UNESP,
UFRJ, UFPE e UFCG.
Avaliação Final
Conforme mencionamos o IME atua em várias frentes (pesquisa, formação de graduados
e mestres, projetos de extensão – olimpíadas e eventos). Em resumo avaliamos que a
participação do IME/UFG no projeto IM-AGIMB está sendo um marco para a consolidação
da pesquisa e ensino (graduação e pós-graduação) no nosso Instituto e nos campi da
UFG. Esta forma de organização com certeza é um marco para o avanço global e
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integrado da matemática brasileira e esperamos estar contribuindo positivamente para o
sucesso deste projeto inovador de excelência acadêmica.
Grupos e Linhas de Pesquisa
Geometria Diferencial
Este grupo está formado por 5 doutores, sendo 3 deles com Pós-Doutorado na UnB. O
líder deste grupo no IME/UFG, é o prof. Walterson Pereira Ferreira.
As linhas de pesquisa são:
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Transformações de Ribaucour e aplicações
Métricas conforme e tensores de Ricci
Superfícies mínimas em espaços de Randers
Uma classe de hipersuperfícies no espaço hiperbólico associadas a aplicações
harmônicas.
Álgebra
O grupo de álgebra está formado por 5 docentes da UFG. A líder do grupo é professora
Shirlei Serconek, doutora com pós-doutorado em Rutgers University – USA.
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Álgebra Não Comutativa
Identidades Polinomiais
Criptografia
Teoria de Números
Teoria de Grupos
Grupos de Bianchi
Transferência de Identidades de Comutadores
Otimização
Este grupo está formado por 5 doutores, sendo que 1 deles, com Pós-Doutorado no
Georgia Institute of Technology – USA. Eles tem trabalhado em conjunto com
pesquisadores do IMPA, da UFPI, COPPE/UFRJ e Georgia Institute of Technology –
USA. O líder deste grupo no IME/UFG, é o prof. Orizon Pereira Ferreira.
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Programação não-linear
Programação semi-definida
Equações Diferenciais Parciais
Este grupo está formado por 4 docentes, sendo que 2 deles, com Pós-Doutorado no IMPA
e North Carolina State University – USA. Eles tem trabalhado em conjunto com
pesquisadores do IMPA, da Unicamp e UnB. O líder deste grupo no IME/UFG, é o prof.
Maurílio Márcio Melo.
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Soluções generalizadas para a Equação de Camassa-Holm
Problemas elípticos quasilineares com crescimento crítico
Problemas de contorno não-lineares
Problemas não-lineares em equações de evolução
Ondas viajantes para um problema de múltiplas reações químicas de combustão em
meios porosos
Probabilidade e Estatística
Este grupo está formado por 2 docentes, sendo os dois doutores pela USP-São Paulo.
Eles tem trabalhado em conjunto com pesquisadores da USP-São Paulo, França. O líder
deste grupo no IME/UFG, é o prof. Oswaldo Scarpa.
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Modelagem estocástica do ritmo da fala
Propriedades assintóticas de um modelo de reação em cadeia
Propriedades assintóticas de um sistema de passeios aleatórios
Sistemas Dinâmicos
Este grupo está formado por 3 docentes, sendo dois doutores pelo IMPA e um pela
Unicamp. O professor Ronaldo Alves Garcia é Pesquisador do CNPq nível 1D. O líder
deste grupo no IME/UFG é Ronaldo Alves Garcia.
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Equações diferenciais da geometria diferencial e sistemas dinâmicos
Estabilidade e bifurcação de campos vetoriais no plano
Dinâmica dos sistemas reversíveis
Órbitas homoclínicas de campos vetoriais reversíveis
Produção Científica
Ano de 2002
1. Garcia, R.A.; Sotomayor, Jorge, Geometric mean curvature lines on surfaces
immersed in R 3, Ann. Fac. Sci. Toulouse Math., (6) 11(3), 377-401, 2002.
2. Garcia, R.A.; da Mota, Jesus C.; de Souza, Aparecido J.; Teixeira, Pedro W.,
Oxidation fronts in a simplified model for two-phase flow in porous media, Seventh
Workshop on Partial Differential Equations, Part I (Rio de Janeiro, 2001), Mat.
Contemp, 22, 67-82, 2002.
3. Garcia, R.A.; Sánchez-Bringas, F., Closed principal lines of surfaces immersed in the
Euclidean 4-space, J. Dynam. Control Systems, 8, 2002.
4. Garcia, R.A.; Sotomayor, Jorge, Umbilic and tangential singularities on configurations
of principal curvature lines, An. Acad. Brasil. Ciênc., 74, 1-17, 2002.
5. Garcia, R.A.; Sotomayor, Jorge, Saddle funnels of vector fields on the plane,
International Conference of 100th anniversary of A. Andronov, 2001, Nizhniui
Novgorod, Progress in Nonlinear Science, Nizhniui Novgorod, RAS, Inst. Appl. Phys.,
1, 361-366, 2002.
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6. da Mota, J.; Dantas, W.; Marchesin, D., Combustion fronts in porous media, SIAM J.
Appl. Math., 62(6), 2175-2198, 2002.
7. Ferreira, O.P.; Lucambio Pérez, L.R. da Cruz Neto, J.X., Contributions to the study of
monotone vector fields, Acta Math. Hungar, 94(4), 307-320, 2002.
8. Ferreira, O.P.; Oliveira, P.R, Proximal point algorithm on Riemannian manifolds,
Optimization, 51(2), 257-270, 2002.
9. Ferreira, O.P.; Svaiter, B.F., Kantorovich's theorem on Newton's method in
Riemannian manifolds, J. Complexity, 18(1), 304-329, 2002.
10. Pina, Romildo; Tenenblat, Keti, On metrics satifying equation Rij-1/2 Kg ij =Tij for
constant tensors T, J. Geom. Phys., 40, 2002.
11. Serconek, Shirlei; Gelfand, Israel; Gelfand, Sergei; Retakh, Vladimir; Wilson Robert
Lee, Hilbert series of quadratic algebras associated with pseudo-roots of
noncommutative polynomials, J. Algebra, 254(2), 279-299, 2002.
12. de Castro, Helvecio Pereira; Noronha, Maria Helena, Homogeneous manifolds in
codimension two revisited, Note Mat., 21(1), 49-57, 2002.
13. Alves, O.S.M.; Machado, F.P.; Popov, S. Yu, Phase transition for the frog model,
Electron. J. Probab, 7(16), 21p. (electronic), 2002.
14. Alves, O.S.M.; Machado, F.P.; Popov, S. Yu, The shape theorem for the frog model,
Ann. Appl. Probab., 12(2), 533-546, 2002.
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Report
Emerging Center
Federal University of Maranhão
Coordinator: Nivaldo Muniz
Historical context and AGIMB contribution
In the last decade we have lost ½ of our faculty due to early retirements; teaching needs
were covered by substitute teachers with low qualifications. Out of our 25 faculty in 2002,
we had only 4 Ph.Ds. and 7 M.Scs. There was no regular research activities and no
Scientific Initiation program. With the impact of IM-AGIMB there was a clear change in
attitude by teachers and students. Our students now want to know what happens after
they get their B.Sc. and several manifest the desire to participate in summer programs.
Our faculty are now actively involved in research. Recently one of our professors returned
from a leave of absence and immediately started to supervise 2 IC students. At the same
time, another professor went to Instituto Politecnico de Milano for his Ph.D.
Motility
We have established and reinforced relations with UNESP, São José do Rio Preto – SP,
Universidade Federal do Ceará – UFC, Universidade de São Paulo and Universidade
Federal do Rio de Janeiro – UFRJ. IM-AGIMB offered support for travel and living
expenses. We have joint research in the areas of Dynamical Systems, Geometry, and
PDEs, the latter with UFRJ.
Infrastructure
Before AGIMB, we had a dozen obsolete microcomputers, but now we were able to obtain
4 new and quite robustly configured ones.
Ongoing activities
We have a committee preparing the “Semana da Matemática” next November, to expose
and give incentives to our activities and results.
Publications
1. F.D. Araruna, G.O. Antunes and L.A. Medeiros, Exact Controllability for a Semilinear
Timoshenko's Model of Beam, Submetido para Eletronic Journal of Qualitative Theory
of Differential Equations, 2004.
2. F.D. Araruna, G.O. Antunes and H.R. Crippa, Hiperbolic Equation with a Resintance
Term and Locally Distributed Damping, Submetido para Nolinear Analysis, 2004.
3. Araujo, M.A.F., Sobre um modelo noa linear para
encontro regional da SBPC, 24ª, 2004.
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a equacao da onda,
Atas do
4. F.D. Araruna, G.O. Antunes and L.A. Medeiros, Exact Controllability for a Semilinear
String Equation in Non Cylindrical Domain, Control and cybernetics, 33 (2), 2004.
5. Horita, V.; Muniz, N. and Sabini, P., Non periodic biffurcations, submetido Ergodic
Theory and Dynamical Systems.
6. Souza, Valeska Martins de; Costa Filho, José Tarcisio and Moraes, Eliúde Trovão.
Controle Ótimo de Sistemas Discretos com Atraso Via LMI. Advances in Intelligent
Systems and Robotics, Laptec, Marília - SP, 2, 147-154, 2003.
7. Souza, Valeska Martins de and Costa Filho, José Tarcisio. Síntese de Controladores
H00 via Programação Semidefinida. VI Simpósio Brasileiro de Automação Inteligente,
Bauru, 467-472, 2003.
8. Araujo, M.A.F.; Cunha, C.A.R.; Pereira, D.C. and Santos, M.L., Exponential Stability for
the Timoshenko system by a two Locally Distributed Dampings, Atas do Seminário
Brasileiro de Análise.
9. Fernandes, D.N. and Garnica, A.V.M. Concepções de Professores Formadores:
exposição e analise do seu sentido doutrinário. Quadrante. Lisboa, XI(2), p.76-98,
Referências adicionais : Portugal/Português. Meio de divulgação, 2003.
10. Fernandes, D.N., O Perfil Profissional dos Técnicos de Nivel Medio que atuam na Área
de Construção Civil no Maranhão. Revista de Educação. São Luis. Referências
adicionais, Brasil/Português. Meio de divulgação, 2003.
11. Fernandes, D.N., Concepções do Professor de Matemática, contribuições para um
referencial teórico. Boletim do GEPEM. Rio de Janeiro, 40, 11-36, 2002.
12. F.D. Araruna, G.O. Antunes and L.A. Medeiros, Semilinear Wave Equation on
Manifolds, Annales de la Faculté de Science de Toulouse, IX (1), 7-18, 2002.
13. G.O. Antunes, F. D. Araruna and L.A. Medeiros, Simultaneous Controllability for a
System with a Resistance Term, Tendências em Matemática Aplicada e
Computacional, 3(1), 31-40, 2002.
14. Souza, Valeska Martins de. Projeto de Controlador Robusto via Programação
Semidefinida. Advances in Logic, Artificial Intelligence and Robotics, SP, 2, 173-180,
2002.
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Report
Emerging Center
Federal University of Pará
Coordinator: Julio S. de Araujo Corrêa
Impact of IM-AGIMB
Our M.Sc. program, which started in 1994, was accredited by CAPES in 2003. This is a
very important development, since Pará comprises a very large region, and our University
provides teaching and training in several campii.
We have presently 10 scientific initiation fellowships. The students are being supervised by
Cristina Lúcia Dias Vaz,Francisco Julio Sobreira de Araujo Corrêa, José Miguel Martins
Veloso, Juaci Picanço da Silva, Mauro de Lima Santos and Silvano Dias Bezerra de
Menezes, all active researchers.
Mobility
AGIMB has supported exchanges with Universidade Estadual de Maringá, Universidade
de Brasília, Universidade Federal de Campina Grande, Universidade Federal de São João
Del-Rei, Universidade Federal de Viçosa with the objective of joint research, and several
trips to participation in events.
Books
Initially the resources were used for undergraduate level books, but since 2003 we have
given priority to graduate/research level materials.
Research
In the last 3 years our production totalized more than 30 articles, some in Journals with
grade A in CAPES-Qualis, like Advances in Differential Equations, Nonlinear Analysis,
Theory, Methods and Applications, Computers and Mathematics with Applications, Applied
Mathematics and Computation, Electronic Journal of Differential Equations, Journal of
Algebra.
Teacher Training
In January and July 2004 we organized courses attended by about 120 teachers, with
excellent receptivity.
Events
IM-AGIMB sponsored the Colóquio Paraense de Matemática, December 2003, with the
participation of Professors Djairo Guedes de Figueiredo, João Lucas Marques Barbosa,
Paolo Picione and Cristina Cunha, we plan to repeat this event in 2004.
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Research areas
All of our 20 faculty have Ph.D. and M.Sc., working in
• Elliptic PDEs
• Control Theory of Evolution Equations
• Navier Stokes equations
• Differential Geometry
• Dynamical Systems
• Bernstein algebras
1. Corrêa, F.J.S.A., Menezes, S.D.B., Existence of Solutions to Nonlocal and Singular Elliptic
Problems Via Galerkin Method, Electron J. Differential Equations, Texas, 19, 1-10, 2004.
2. Corrêa, F.J.S.A., On a Class of Nonlocal and Nonvariational Problems, Journal of Nonlinear
Analysis: Series A Theory and Methods, Grã-Bretanha, 2004.
3. Corrêa, F.J.S.A., On a Class of Problems Involving a Nonlocal Operator, Applied
Mathematics and Computation, 147, 475-489, 2004.
4. Corrêa, F.J.S.A., Alves, C.O., Fu, M.T., Positive Solutions for a Quasilinear Elliptic Equation
of Kirchhoff Type, Computers and Mathematics with Applications, 2004.
5. Santos, M.L., Oliveira Júnior, F.M., A boundary condition with memory for Kirchhoff plates
equations, Applied Mathematics and Computations, 148, 475-496, 2004.
6. Santos, M.L., Raposo, C. A., Ferreira, J., Existence and uniform decay for a nonlinear beam
equation with nonlinearity of Kirchhoff type in domains with moving boundary. Abstract and
Appied Analysis, 2004.
7. Santos, M.L., M. M. Cavalcanti, Cavalcanti, V. N. D., Existence and uniform decay rates of
solutions to a degenerate system with memory conditions at the boundary, Applied
Mathematics and Computations, 150, 439-465, 2004.
8. Santos, M.L., Raposo, C.A., Ferreira, J., N.N.O., Castro. Exponential stability for the
Timoshenko system with two weak dampings, Applied Mathematics Letters, 2004.
9. Santos, M.L., Raposo, C.A., Ferreira, J., On Global Solvability and Asymptotic Behavior of a
Nonlinear Coupled System with Memory Condition at the Boundary. Bulletin of the Belgian
Mathematical Society-Simon Stevin, Bélgica, 11, 297-313, 2004.
10. Santos, M.L., Ferreira, J., Matos, M.P., Stability for beam equations with memory in
noncylindrical domains, Math. Meth. Appl. Sci., England, 27(3), 1493-1506, 2004.
11. Correa,F.J., Menezes, S.D.B., Existence of Solutions to Nonlocal and Singular Elliptic
Problems via Galerkin Method, Eletronic Journal of Differential Equations, 19, 1-10, 2004.
12. Correa,F.J., Menezes, S.D.B., On a Class of Problems Involving a Nonlocal Operator,
Applied Mathematics and Computation, 147, 475-489, 2004.
13. Boldrini, J.L., Vaz, C.L.D., Existence and regularity of solutions of a phase field model for
solidification with convection of pure materials in two dimensions, Eletronic Journal of
Differential Equations, 109, 1-25, 2003.
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14. Corrêa, F.J.S.A., Goncalves, J.V.A., Melo, A.L., On Positive Radial Solutions of Quasilinear
Elliptic Equations. Nonlinear Analysis, Theory, Methods and Applications, Grã-Bretanha,
52(2), 681-701, 2003.
15. J. Picanço, On the invariance of subspaces in some baric algebras. On the invariance of
subspaces in some baric algebras/Revista Proyecciones, Chile, 2003.
16. Santos, M.L., Ferreira, J., Asymptotic behaviour for wave equations with memory in a
noncylindrical domains, Communications on Pure and Applied Analysis, USA, 2(4), 511-520,
2003.
17. Santos, M.L., Ferreira, J., Matos, M.P., Bastos, W.D., Exponential decay for Kirchhoff wave
equation with nonlocal condition in a noncylindrical domain, Mathematical Computer
Modelling, 2003.
18. Santos, M.L., Ferreira, J., Pereira, D.C., Raposo, C. A., Global existence and stability for
wave equation of Kirchhoff type with memory condition at the boundary, Journal of Nonlinear
Analysis, Inglaterra, 54, 959-976, 2003.
19. Santos, M.L., Raposo, C.A., Soares, U.R., On nonlinear coupled system with nonlocal
boundary conditions, Bulletin of Parana's Mathematical Society, Brasil, 20, 1-24, 2003.
20. Santos, M.L., Rivera, J.E.M., Polynomial stability to three-dimensional magnetoelastic
waves, Acta Applicandae Mathematicae, Holanda, 76, 265-281, 2003.
21. Santos, M.L., Ferreira, J., Pereira, D.C., Stability for a coupled system of wave equations of
Kirchhoff type with nonlocal boundary conditions, Electron J. Differential Equations, 85, 1-17,
2003.
22. Santos, M.L., Ferreira, J., Stability for a system of wave equations of Kirchhoff with coupled
nonlinear and boundary conditions of memory type, Advances in Differential Equations, 8(7),
873-896, 2003.
23. Menezes, S.D.B., Approximate Controllability for the Semilinear Heat Equation in RN
Involving gradient terms, Computational and Applied Mathematics, 22(1), 123-148, 2003.
24. Menezes, S.D.B., Oliveira, E., Pereira, D.C., Ferreira, J., Existence, Uniqueness and
Uniform Decay for the Nonlinear Beam Degenerate Equation with Weak Damping, Applied
Mathematics and Computation, 2003.
25. Menezes, S.D.B., Ferrel, J.L., Medeiros, L.A., Finite Aproximate Controllability for Semilinear
Heat Equation in Noncylindrical Domains, Anais da Academia Brasileira de Ciências, 2003.
26. Menezes, S.D.B., Finite-Dimensional Null Controllability in RN for a Semilinear Heat
Equation, Analysis, 2003.
27. Menezes, S.D.B., Ferrel, J.L., Medeiros, L.A., Remarks on Null Controllability for Semilinear
Heat Equation in Moving Domains. Eletronic, Journal of Qualitative Theo of Differential
Equations, 16, 1-32, 2003.
28. Oliveira, J.C.F., Oscillations in a van der Pol equation with delayed argument, Journal of
29. Santos, M.L., Decay rates for solutions of a Timoshenko system with a memory condition at
the Boundary, Abstract And Applied Analysis, 7(10), 531-546, 2002.
30. Santos, M.L., Decay rates for solutions of a system of wave equations with memory.
Electron J. Differential Equations, 38, 1-17, 2002.
161
31. Santos, M.L., Decay rates for solutions of semilinear wave equations with a memory
condition at the boundary, Electronic Journal of Qualitative Theory of Differential Equations,
7, 1-17, 2002.
32. Santos, M.L., Ferreira, J., Global existence for a quasilinear hyperbolic equation in a
noncylindrical domain, International Journal of Pure and Applied Mathematics, 2002.
33. Menezes, S.D.B., Ferrel, J.L., Medeiros, L.A., Remarks on null controllability for heat
equation in thin domains, Computational and Applied Mathematics, 21(1), 47-65, 2002.
34. Menezes, S.D.B., Ferrel, J.L., Medeiros, L.A., Vibrations of Elastic Strings-Part One, Journal
of Computational Analysis and Applications, 4(2), 91-127, 2002.
35. Menezes, S.D.B., Ferrel, J.L., Medeiros, L.A., Vibrations of Elastic Strings-Mathematical
Aspects.Part Two, Journal of Computational Analysis and Applications, 4(3), 211-263, 2002.
162
Report
Emerging Center
Federal University of Paraíba
Coordinator: João M. Bezerra do Ó
Researchers
João Marcos Bezerra do Ó; Everaldo Souto de Medeiros; Pedro Hinojosa Vera; Ana Maria
Amarillo Bertone (ex-participant)
Scientific Initiation program
We had only 4 CNPq-PIBIC scholarships, but with the impact of IM-AGIMB, we have now
11 more. We have 2 volunteering students (without fellowships) and 13 high school
students.
Research: Mobility and Productivity
We have now interchanges with Università di Milano - Itália, Chinese Academy of
Sciences - China, Queensland University - Australia, USACH - Chile, UTA - Chile,
UNICAMP, UnB, UFV, UFMG. As a result our productivity reached a quite good average.
Professor
João Marcos Bezerra do Ó
Everaldo Souto de Medeiros
Pedro Hinojosa
Institution
USACH/Chile
UNICAMP
UnB
UFC
UFCG
UFCG
UNICAMP
UFMG
IMPA
UFC
Date
2002
2002, 2003, 2004.
2003, 2004.
2003, 2004.
2002; 2003, 2004
2002; 2003; 2004
2004
2003
2004
2002; 2003; 2004
Scientific Events
We promoted events at all levels, starting with the Scientific Initiation-Millennium - UFPB
in September 2002 and September 2003, the international workshop “Millennium
Workshop in Eliptic Equation” (http://abel.mat.ufpb.br/~jmbo/simposio) in January 2004,
and the Curso de Aperfeiçoamento para professores de Matemática do Ensino Médio,
July 2004. We have 3 regular seminars, in the Junior-Scientific Initiation, Scientific
Initiation, and Scientific Initiation -M.Sc levels.
Infrastructure
We used IM-AGIMB resources mainly to purchase books.
163
Publications/Scientific Initiation projects/Visitors. See the detailed report.
1. Medeiros, E.S., Alves, Claudianor Oliveira, Carrião, Paulo Cesar, Multiplicity of
solutions for a class of quasilinear problem in exterior domains with Neumann
conditions, Abstract and Appied Analysis, 3, 251-268, 2004.
2. Marivaldo Pereira Matos, Stability for the Beam Equation with Memory in NonCilindrical Domains, Math. Methods in the Applied Sciences, 27(13), 1493-1506, 2004.
3. Machado, Liliane dos Santos, Moraes, Ronei Marcos de, Using Fuzzy Hidden Markov
Models for Online Training Evaluation and Classification in Virtual Reality Simulators,
International Journal on General Systems, 33(2-3), 281-288, 2004.
4. Marivaldo Pereira Matos, Hidden Regularity for the Parabolic-Hyperbolic Equations,
2004.
5. do Ó, João Marcos; Lorca, Sebastian; Ubilla, Pedro, Multiparameter Elliptic in Annular
Domains, Journal of Mathematical Analysis and Applications, 2004.
6. do Ó, João Marcos; Lorca, Sebastian; Ubilla, Pedro, Local Superlinearity for Elliptic
Systems Involving Parameters, Journal of Differential Equations, 2004.
7. do Ó, João Marcos; Ruf, Bernhard, On a Schrödinger equation with periodic potential
and critical growth in R 2, NoDEA, 2004.
8. de Figueiredo, Djairo G..; do Ó, João Marcos; Ruf, Bernhard, Critical and Subcritical
Elliptic systems in dimension two, Indiana University Mathematical Journal, 2004.
9. Machado, Liliane dos Santos, Zuffo, Marcelo Kñorich, Development and Evaluation of
a Simulator of Invasive Procedures in Pediatric Bone Marrow Transplant, Studies in
Health Technology and Informatics, Amsterdam, 94, 193-195, 2003.
10. Machado, Liliane dos Santos, Melo, Ana Cláudia Oliveira, Moraes, Ronei Marcos de,
Gaussian Mixture Models for Supervised Classification in Remote Sensing Images,
Lecture Notes in Computer Science, 2905, 440-447, 2003.
11. Moraes, Ronei Marcos de, Machado, Liliane dos Santos, Hidden Markov Models for
Learning Evaluation in Virtual-Reality Simulators, International Journal of Computers
Applications, Canadá, 25(3), 212-215, 2003.
12. Machado, Liliane Dos Santos, Moraes, Ronei Marcos de, Online Training Evaluation in
Virtual Reality Simulators Using Gaussian Mixture Models, Studies in Health
Technology and Informatics, Amsterdam, 94, 42-44, 2003.
13. do Ó, João Marcos, Ubilla, Pedro, A multiplicity result for a class of superquadratic
Hamiltonian systems, Electron J. Differential Equations, 15, 1-14, 2003.
14. do Ó, João Marcos, UbillaPedro, Multiple Solutions for a class of Quasilinear Elliptic
Problems, Proceedings of the Royal Society of Edinburgh Section A-Mathematics,
Edinburgh, 46(1), 159-168, 2003.
15. do Ó, João Marcos, Bertone, Ana Maria, On a class of semilinear Schrödinger
equations involving critical growth and discontinuous nonlinearities, J. of Nonlinear
Theory Methods and Applications, 54(5), 885-906, 2003.
16. do Ó, João Marcos, Alves, C. O., Miyagaki, O, On a class of singular biharmonic
problems involving critical exponents, Journal of Math. Analysis and Applications,
277(1), 12-26, 2003.
164
17. do Ó, João Marcos, Medeiros, Everaldo Souto de, Remarks on least energy solutions
for quasilinear elliptic problems in ℜN, Electron J. Differential Equations, 83, 1-14,
2003.
18. do Ó, J. M. B., Medeiros, E. S. and Everaldo S. Medeiros, Remarks on least energy
solutions for quasilinear elliptic problems in ℜ N. Electron J. Differential Equations, 83,
1-14, 2003.
19. Machado, Liliane Dos Santos, Netto, Antonio Valério, Oliveira, Maria Cristina Ferreira
de. Realidade Virtual: Definições, Dispositivos e Aplicações, REIC-Revista Eletrônica
de Iniciação Científica, http://www.sbc.org.br/reic, 2(1), 1-30, 2002.
20. Machado, Liliane Dos Santos, Mello, André Nedel De, Odone Filho, Vicente, Zuffo,
Marcelo Kñorich, Virtual Reality Simulation of Pediatric Bone Marrow Harvest for
Transplant, Medical And Pediatric Oncology, 39(4), 282-82, 2002.
21. Machado, Liliane Dos Santos, Netto, Antonio Valério, Oliveira, Maria Cristina Ferreira
de. Realidade Virtual - Fundamentos e Aplicações, Florianópolis, Visual Books, 1,
p.96, 2002.
22. Arancibia, J.F.R., Vainsencher, I., Canonical Curves in P3, Proceedings of the London
Mathematical Society, London, 3(85), 333-366,2002.
23. Marivaldo Pereira Matos, Equações Diferenciais de 2ª Ordem, Seção para o site do
livro "Cálculo, G. B. Thomas", Addison Wesley, 2003.
24. Assis, J.G., Bezerra, V.B., Non-adiabatic Berry's Quantun Phases in Anisotropic
Universes, Mod.Phys. Lett. A, 117(25), 1665-1672, 2002.
25. Milton de Lacerda Oliveira, Study of a model for the equations of inserted elastic string
in a thermal environments by Oliveira, Feitosa and Matias.
26. do Ó, João Marcos, Alves, C.O., Miyagaki, O., On a class of singular biharmonic
problems involving critical exponents. Journal of Mathematical Analysis and
Applications, 272 (2), 393-406, 2002.
27. do Ó, João Marcos, Ruf, B., Figueiredo, D., On an inequality by N. Trudinger and J.
Moser and related elliptic equations, Communications on Pure and Applied
Mathematics, 55(2), 135-152, 2002.
28. do Ó, João Marcos, Chabrowski, J., On semilinear elliptic equations involving concave
and convex nonlinearities. Mathematische Nachrichten, 233-234, 55-76, 2002.
29. do Ó, João Marcos, Chabrowski, J., On some fourth-order semilinear elliptic problems
in RN, Journal of Nonlinear Analysis, EUA, 49(6), 861-884, 2002.
30. do Ó, João Marcos, Alves, C. O., Positive solutions of a fourth-order semilinear
problem involving critical growth, Advanced Nonlinear Studies, EUA, 2(4), 437-458,
2002.
31. Medeiros, E. S., On the Existence of ground state for a Quasilinear Eliptic problem in
ℜN. In: 55 Seminário Brasileiro de Análise, 2002, Uberlândia, Anais do 55 Seminário
Brasileiro de Análise, 1, 249-253, 2002.
32. Hinojosa, Pedro A., Graphs with Constant Mean Curvature in the 3-Hyperbolic Space,
Anais da Academia Brasileira de Ciências, 74(3), 371-377, 2002.
33. Hinojosa, Pedro A., Surfaces of Constant Mean Curvature in 3-Space Orthogonal to a
Plane along its Boundary. Anais da Academia Bras. de Ciências, 74(1), 32-35, 2002.
165
34. Bertone, A.M.A., Abreu, J.V.G., Alves, C., Discontinous Elliptic Problems, Journal of
35. Bertone, A.M.A., Abreu, J.V.G., Discontinuous Elliptic Problems in ℜ N lower and upper
solutions and variational principles, Discrete and Continuous Dynamical Systems,
2000.
36. Bertone, A.M.A., Remark on Discontinuos Elliptic Problems in RN. In: 55 Seminário
Brasileiro de Análise, Atas do 55 Seminário Brasileiro de Análise, 2002.
37. Bertone, A.M.A., Vieira, O., Um Teorema de link para Funcionais Gateaux
Diferenciávis. In: 56º Seminário Brasileiro de Análise, Anais do 56º SBA, UFF, 2002.
166
Report
Emerging Center
Federal University of Paraná
Coordinator: Jin Yuan
Impact of AGIMB
There was a great stimulus for our research and teaching activities since 2002,
exemplified by the recognition by Capes of our M.Sc. program, the improvement of our
library and computational facilities.During the 3 years of this project, 9 professors of our
Department finished their Ph.D., 4 are underway, and we have hired 7 Ph.D., totalizing 16
new members, thus renewing 1/3 of the faculty. Several of our members had their work
prized at different levels.
Mobility
We have interacted with the Algebra teams of USP and UNICAMP, with the Scientific
Computing teams of UFSC, UNICAMP and IMPA, with the PDE teams of UEM, UFRJ e
LNCC, with the Mathematical Physics teams of UNICAMP, USP e UFSC, and Analysis
group of UFSCar.
Events supported by IM-AGIMB
•
Second International Workshop on Numerical Linear Algebra, Optimization and
Numerical Methods for PDE's (2001), 100 participant s.
• I Colóquio Regional da SBM (2002), 400 participants.
• II Semana de Matemática Industrial e XI Semana de Matemática (2002), 160
participants.
• I Workshop em Modelagem e Métodos Matemáticos no Setor Energético (2004),
expected 100 participants.
AGIMB financed 24 fellowships. Six of them are already in a M.Sc. program. Our recent
M.Sc program has already graduated 3 M.Sc, one of them working towards Ph.D. at
Unicamp and the other at USP. In another program of Numerical Methods in Engineering,
20 students were supervised by us
Teacher training
The Videoconferences training series had the participation of 120 teachers in our State.
Research lines
• Mathematical Physics
• Mathematical Education
• Optimization and Scientific Computing
167
•
•
•
Fuzzy Topology
Operational Research
1. L.-Z. Hu, L. Hu and A.S. Sant'Anna, Born-Infeld action on discrete spaces, International
Journal of Theoretical Physics, 43, 315-321, 2004.
2. A. S. Sant'Anna and A. Sartorelli, PRIMOS está em P, Scientific American Brasil, 20,
18-19, 2004.
3. A. S. Sant'Anna, E se um aluno perguntar: Maxwell ou Weber? Scientific American
Brasil, 26, 20-20, 2004.
4. R. L. Viana, J. R. R. Barbosa and C. Grebogi, Unstable dimension variability and
codimension-one bifurcations of two-dimensional maps, Physics letters A, 321, 244251, 2004.
5. A. G. Volkov, N. C. A. da Costa and O. Bueno, Outline of a paraconsistent category
theory, Alternative Logics. Do Sciences Need Them? (edited by Paul Weingartner,
Berlin, Springer-Verlag), 95-114, 2004.
6. R. C. Wrede and M. Spiegel, Cálculo Avançado, Bookman, Porto Alegre (traduction
and apresentation by A. S. Sant'Anna), 2004.
7. J.Y. Yuan, G.H. Golub, R.J. Plemmons and W. Cecilio, Semi-conjugate direction
methods for real positive definite systems, BIT, 2004.
8. J.Y. Yuan and P.Y. Yalamov, A method for constructing diagonally dominant
preconditioners based on Jacobi rotations, Applied Mathematics and Computation,
2004.
9. G. Ducati and S. De Leo, Solving simple quaternionic differential equations, Journal of
Mathematical Physics, 44, 2224-2233, 2003.
10. Y.-H. Dai, J. M. Martinez and J. Y. Yuan, An increasing-angle property of the conjugate
gradient method and the implementation of large scale minimization algorithms with
line searches, Numerical Linear Algebra with Applications, 10, 323-334, 2003.
11. Yuhong Dai and Jin Yun Yuan, Study on Semi-Conjugate Direction Methods for
Nonsymmetric Systems, International Journal for Numerical Methods in Engineering,
2003.
12. L.-Z. Hu and A. S. Sant'Anna, Gauge theory on a discrete noncommutative space,
International Journal of Theoretical Physics, 42, 635-647, 2003.
13. L.-Z. Hu and A. S. Sant'Anna, Spinor representation of electromagnetic fields on
noncommutative spaces, International Journal of Theoretical Physics, 42, 499-506,
2003.
14. M. Muniz and S. Costa, Labelings of Lee and Hamming Spaces, Discrete Mathematics,
260C, 119-136, 2003.
15. J. J. Rossetto, Análise de modelos de filtros mecânicos para eritrócitos. Doctoral
Thesis, 001, CPGEI/CEFET-PR, 2003.
168
16. A. S. Sant'Anna and C. Garcia, Gravitation in Hertz mechanics. Foundations of Physics
Letters, 16, 559-572, 2003.
17. A. S. Sant'Anna, D. Krause and F. A. Doria, Newton da Costa. Scientific American
Brasil, 13, 22-24, 2003.
18. Wen-yu Sun, Jin Yun Yuan and Ya-xiang Yuan, Conic trust region method for linearly
constrained optimization. Journal of Computational Mathematics, 21(3), 295-304, 2003.
19. A. S. Sant'Anna, A discretização do tempo, Scientific American Brasil, 13, 2003.
20. A. S. Sant'Anna, Lógica paraconsistente. Scientific American Brasil, 12, 2003.
21. A. S. Sant'Anna, Matemática e senso crítico. Scientific American Brasil, 14, 2003.
22. A. S. Sant'Anna, O que é um Axioma. Edited by Manole, Barueri, 2003.
23. F. Safier, Pré-Cálculo. Coleção Schaum, Bookman, traduction and apresentation of A.
S. Sant'Anna, 2003.
24. A. Sartorelli, Uma construção dos números reais por meio decimais, Research Report,
Department of Mathematics, UFPR, Curitiba - PR, 2003.
25. R. L. Viana, S. E. de S. Pinto, J. R. R. Barbosa and C. Grebogi, Pseudo-deterministic
chaotic systems. International Journal of Bifurcations and Chaos, 11, 1-19, 2003.
26. P. Yalamov and J. Y. Yuan, A successive least squares method for structured total
least squares problems. Journal of Computational Mathematics, 22(4), 463-472, 2003.
27. M. M. S. Alves, J. R. Gerônimo, R. Palazzo Júnior, S. I. R. Costa, J. C. Interlando and
M. C. Araújo, Relating propelinear and binary G-linear codes, Discrete Mathematics,
243, 1-3 and 187-194, 2002.
28. E. R. Alvares, Mergulhos de quivers com translação em quivers de tipo Z Delta. Ph. D.
Thesis, University of São Paulo, Brazil, 2002.
29. R. Biloti, L. T. Santos and M. Tygel, Multiparametric traveltime inversion, Stud.
Geophysics Geod., 46, 177-192, 2002.
30. W.A.G. Cecilio, C.J. Cordeiro, I. Milleo, C. Santiago, R. Zanardini and J. Y. Yuan, A
note on polynomial interpolation. International Journal of Computer Mathematics,
79(4), 465-471, 2002.
31. N. C. A. da Costa and A. S. Sant'Anna, The mathematical role of time and spacetime in
classical physics. Foundations of Physics Letters, 14, p.553-563, 2002.
32. N. C. A. da Costa and A. S. Sant'Anna, Time in Thermodynamics. Foundations of
Physics, 32, 1785-1796, 2002.
33. Yuhong Dai, J. Y. Yuan and Yaxiang Yuan, Modified two-point stepsize gradient
methods for unconstrained optimization. Computational Optimization and Applications,
22(1), 103-109, 2002.
34. G. Ducati, Operadores diferenciais quaterniônicos e aplicações em física. Tese de
doutorado, Departamento de matemática aplicada, IMECC, Unicamp, 2002.
35. C. C. Gonzaga and M. Cardia, Properties of the central points in linear programming
problemas. Technical Reports, Department of Mathematics, Federal University of
Santa Catarina, Brazil, 2002.
169
36. C. C. Gonzaga and M. Cardia, Using the central path for computing the analytic center
of a polytope. Technical Report, Department of Mathematics, Federal University of
Santa Catarina, Brazil, 2002.
37. C. C. Gonzaga, E. Karas and M. Vanti, A globally convergent filter method for
nonlinear programming. Technical report, Department of Mathematics, Federal
University of Santa Catarina, Brazil, 2002.
38. G.H. Golub and J. Y. Yuan, Symmetric-Triangular decomposition and its applications part I: theorems and algorithms, BIT, 42(4), 814-822, 2002.
39. J. Hounie and E. R. da Silva, A similarity principle for locally solvable vector fields, J.
Math. Pures Appl. 81, 715-746, 2002.
40. L.-Z. Hu and A. S. Sant'Anna, Connes' spectral triple and U(1) gauge theory on finite
sets, Journal of Geometry and Physics, 42, 296-306, 2002.
41. E. Karas, Exemplos de trajetória central mal comportada em otimização convexa e um
algoritmo de filtros para programação não linear. Dotoral Thesis, Universidade Federal
de Santa Catarina, Brasil, 2002.
42. E. Karas, Exemples de chemins centraux non-réguliers et un algorithme de filtre pour
l'optimisation non-linéaire. Ph. D. Thesis, Université Paris I, Panthéon-Sorbonne,
France, 2002.
43. S. De Leo, G. C. Ducati and C. C. Nishi, Quaternionic potentials in non relativistic
quantum mechanics, Journal of Physics A, 35, 5411-5426, 2002.
44. J. J. Rossetto and P. J. Abatti, Análise da passagem da célula vermelha do sangue
através de poros cilíndricos, TEMA-Tendências em Matemática Aplicada e
Computacional, Seleta do XXIV CNMAC, 3(1), 193-202, 2002.
45. J. J. Rossetto and P. J. Abatti, Determinação da habilidade da célula vermelha do
sangue para transpor dois poros cilíndricos, Bioingeniería y Física Médica Cubana,
2(2), 25-35, 2002.
46. C. Santiago and J.Y. Yuan, Modified ST decomposition and numerical experiments,
Numerical Algorithms, 2002.
47. A.S. Sant'Anna, Some Problems Concerning Definitions in Mathematics and Physics.
Boletim da Sociedade Paranaense de Matemática, 20, 21-28, 2002.
48. J.H. Yin and J.Y. Yuan, Note on stationary iterative methods by SVD, Applied
Mathematics and Computation, 127, 327-333, 2002.
170
Report
Emerging Center
Federal University of Piauí
Coordinator: João Xavier da Cruz Neto
Impact of AGIMB
We have been able to purchase computers for all professors linked to AGIMB, and
upgraded the Teaching laboratory. We have purchased all collections of SBM and several
classical texts. In the research level, we have increased our mobility to other centers
(GATECH-USA, IMPA, UFRJ, UFF, UFC, UFG, UFPb, USP, UNESP), and participation in
national and international events. Although we do not have a graduate program, AGIMB
has been instrumental to refer several of our students to other Institutions.
Scientific Initiation and M.Sc. Program
IM-AGIMB allowed us to have 12 scientific initiation students with fellowships, participant
actively in weekly seminars. In the near future we hope to establish a M.Sc, program.
Teacher Training
In this area we have promoted a true “revolution” in the states of
We have supervised mostly teachers from the rural areas:
ANO / SEMESTRE
2002/2
2003/1
2003/2
2004/1
2004/2
Piauí and Maranhão.
TOTAL
50
72
96
140
170
We would like to propose that this training program could evolve to a M.Sc. program, tied
to incentives such as better salaries.
1. Clark, M. R., Clark, H. R., Flutter Panel Equation in Noncylindrical Domain. Southwest
Journal of Pure and Applied Mathematics. Oklahoma-Eua, 1-03(16), 152-168, 2003.
2. Clark, M. R., Lima, O. A., Existence of Solutions for a Variational Unilateral System.
Electron J. Differential Equations, 1-18, 2002.
171
3. Clark, M. R., Maciel, A. B., On a Mixed Problem for a Nonlinear Kxk System.
International Journal of Applied Mathematics. Sófia-Bulgária, 9, 201-218, 2002.
4. CLARK, M. R., On a Kirchhoff Equation in Noncylindrical Domain. To Appear in
Nonlinear Analysis.
5. Cruz Neto, J. X., Ferreira, O. P., Perez, L. R. L. Contributions to the Study of Monotone
Vector Fieds. Acta Math. Hungar. Hungria, 94(4), 323-336, 2002.
6. Cruz Neto, J. X., Ferreira, O. P. and Monteiro, R.D.C, Asymptotic behavior of the
central path for a special class of degenerate SDP problems, Mathematical
Programming.
7. Burachik, R.S and Lopes, J. O. A convergence result for an outer approximation
scheme, Computational and Applied Mathematics, 22(3), 397-409, 2003.
8. Burachik, R.S., Lopes, J. O. and Svaiter, B. F. An Outer Approximation Method for the
Variational Inequality Problem, Siam Journal on Control and Optimization.
9. Santos, Newton Luis. Manifold with ideal boundaries of different dimensions, Journal of
Mathematics, 40(2), June 2003.
10. Lima, Barnabé Pessoa; Bessa, Gregório Pacelli and Montenegro, José Fábio,
Eigenvalues estimates for operators in divergence form. Submitted for publication.
11. Costa, Otávio de Oliveira, A Normal Form to Hamilthonian System, Journal SBMAC.
172
Report
Virtual Emerging Center
Federal Universities of Viçosa, Uberlândia, São João del Rei and Ouro Preto
Coordinator: Olímpio Miyagaki
Objective
Research, formation of students and hiring at the Universities: Federal de Viçosa, Federal
de Uberlândia, Federal de São João Del Rei, Federal de Ouro Preto.
Areas
Analysis, Algebra, Nonlinear dynamics, Differential Geometry, Singularity theory, and
Differential Equations (ordinary and partial).
Members
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Luiz Cláudio Pereira, UFV, Doutor UNB 1998, Applied Mathematics
Margareth da Silva Alves, UFV, Doutor, UFRJ, 1994, Analysis/EDP
Marinês Guerreiro, UFV, PhD, Univ. Manchester 1997, Algebra
Sandro Vieira Romero, UFV, Doutor IME-USP 2001, Applied Mathematics
Simone Maria de Moraes, UFV, Doutor UNICAMP, 2002, Geometry and Topology
Cícero Fernandes de Carvalho, UFU, Doutor IMPA 1994, Pos-Doc Harvard University
1998, Algebraic Geometry
Geraldo Márcio de Azevedo Botelho, UFU, Doutor UNICAMP 1995, Analysis
Jocelino Sato, UFU, Doutor, UFCe, 2000, Geometry
Márcio José Horta Dantas, UFU, Doutor UFRJ 1988- Applied Mathematic
Walter dos Santos Motta Junior, UFU, Doutor ICMSC-USP 1992, Topology
Francinildo Nobre Ferreira, UFSJ, Doutor UNB 1999, Geometry
Mário Dávila, UFSJ, Doutor UFRJ 1995, Analysis/EDP
Adilson Vieira Brandão, UFOP, Doutor, UNICAMP 1998, Analysis/Optimization
Antônio Luis Rosa, UFOP, Doutor, USP 2000, Algebra
Felipe Rogério Pimentel, UFOP, Doutor, UNICAMP 2003, Applied Mathematic
Gonçalo Astorga Tapia, UFOP, Doutor, USP 2003, Analysis
João Luís Martins, UFOP, Doutor, UNICAMP 2000, Applied Mathematic/Geophysic
Paulo Marcelo Dias de Magalhães, UFOP, Doutor, UFRJ 1994, Analysis/EDP
Impact of AGIMB
Besides a much increased mobility, we have improved the computational and library
resources at every institution. See the detailed report.
173
Some Activities
We promoted, in the first week of September 2004, the first regional Olympiad, the first
Workshop in singularity theory, differential equations and geometry (August 2004), an
Encounter with K1-12 teachers (October 2004).
We obtained 12 fellowships. The projects are described in detail in our full report.
1. Botelho, G.M.A., Pellegrino, D.M., Dominated polynomials on Lp-spaces, Archiv. Der
Mathematik, 2004.
2. Botelho, G.M.A., Ideals of polynomials generated by weakly compact operators, Note
Di Matematica, 2004.
3. Abreu, E.M., Miyagaki, O.H., A Robin problem for a class of quasilinear operators and
a related minimizing problem, J. of Nonlinear An. Theory Methods and Applications,
2004.
4. Alves, C.O., Demorais Filho, D.C., Miyagaki, O.H., Multiple solutions for an elliptic
system on bounded and unbounded domains, Journal of Nonlinear Analysis, 56, 555568, 2004.
5. Figueiredo, D.G., Miyagaki, O.H., Multiplicity of non-radial solutions of critical elliptic
problems in an annulus, Royal Soc. Edinburgh, Proc. A. Edinburgh, 2004.
6. Alves, C.O., Carriao, P.C., Miyagaki, O.H., On a class of elliptic systems involving Nfunctions, Applied Mathematics Letters, 2004.
7. Alves, C.O., Bezerra, J.M., Miyagaki, O.H., On nonlinear perturbations of a periodic
elliptic problem in R2 involving critical growth, J. of Nonlinear. An. Theory Methods and
Applications, 56(5), 781-791, 2004.
8. Moraes, S.M., Romero-Fuster, M.C., Sánchez-Bringas, F., Principal configurations and
umbilicity of submanifolds in RN, Bulletin of the Belgian Mathematical Society-Simon
Stevin, 2004.
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175
Post-Doctoral Fellowships
INSTITUTION
NAME
PERIOD
IMPA
Adelailson Peixoto da Silva
1-Mar-04
31-Jul-04
IMPA
Alexander Eduardo Arbieto Mandoza
1-Jun-04
30-Nov-04
UFC
Antonio Caminha Muniz Neto
1-Mar-04
30-Nov-04
UFC
Cleon da Silva Barroso
1-Mar-04
30-Nov-04
UNICAMP
Edson Alex Arrázola Iriarte
1-Mar-04
30-Nov-04
USP
Fuensanta Aroca Bisquert
1-Apr-04
30-Nov-04
German Jesus Lozada Cruz
1-Mar-04
31-Jul-04
UFPE
Giuseppe Borrelli
1-May-04
30-Nov-04
IMPA
Glauco Valle da Silva Coelho
1-Jul-03
1-Mar-04
USP
Jawad Snoussi
1-Jun-04
30-Nov-04
IMPA
Luciano Irineu de Castro Filho
1-Mar-04
30-Jun-04
UFSC
Marcia Regina Barcellos Vianna Vanti
1-Oct-03
30-Nov-04
IMPA
Milton David Jara Velenzuela
1-Jun-04
30-Nov-04
IMPA
Milton dos Santos Braitt
1-Jul-02
31-Jul-04
IMPA
Paul Krause
1-Jul-02
30-Jan-03
UNB
Wang Qiaoling
1-Mar-04
1-Jun-04
IMPA
William Artiles Roqueta
1-Jul-04
30-Nov-04
UNESP
176
Scientific Initiation Fellowships
NAME
AILTON RIBEIRO DE ASSIS
ALCIDIA DUTRA LOPES
ALENE ALCANTARA REIS
ALESSANDRA LEITE BATISTA
ALESSANDRO GAIO CHIMENTON
AMANDA SILVA MARQUES VILARINS
ANA CRISTINA BITTENCOURT DE JESUS
ANA RITA CAETANO BOCHINI
ANDERSON CARVALHO DOS SANTOS
ANDERSON DAVID DE SOUZA CAMPELO
ANDERSON LUIS ALBUQUERQUE DE ARAUJO
ANTONIO PEREIRA DE FARIAS FILHO
ARIANE PIOVEZAM ENTRINGER
ARISTÓTELES MAURÍCIO PEREIRA DOS SANTOS
AURELIO SOARES DE CARVALHO
BARBARA COSTA DA SILVA
BRICELA DE ARRUDA FRANCHINI
BRUNO MENDONÇA REY DOS SANTOS
CARLA CRISTINA DE SOUZA TAVARES
CARLOS ALBERTO SILVA DOS SANTOS
CAROLINE ELISA MURR
CRISTIANY DE MOURA BARROS
DANIEL MENDES AZERÊDO
DANÚBIA JUNCA
DAVI ALISSON DOS SANTOS NOBREGA
DIOGO DE SANTANA GERMANO
DIOGO DINIZ PEREIRA DA SILVA E SILVA
DOUGAS ARAUJO VICTOR
DOUGLAS DE OLIVEIRA MAIA
EDNALDO OLIVEIRA DA SILVA JUNIOR
ELIANE DA SILVA DOS SANTOS
EMERSON SOUZA SILVA
ENNE KAROL VENANCIO DE SOUSA
ERIKSON ALEXANDRE FONSECA DOS SANTOS
EUGÊNIO MENDES M. FILHO
EVALDO DE ALMEIDA ALBUQUERQUE
FABIANA CHAGAS
FABIO LUIZ BORGES SIMAS
FANG CHOU LEE
FERNANDA MOCELIN SCHENA
FLANK DAVID MORAIS BEZERRA
FLÁVIA FERREIRA RAMOS
FRANCIANE JOSE DA SILVA
FRANCISNMARA FERNANDES GUERRA SILVA
177
INSTITUTION
UFPB
UFPA
UFBA
UFPR
UFPR
UFAL
UFBA
UFSJ
UFAL
UFPA
UFPA
UFPB
UFV
UFPI
UFES
UFBA
UFV
UFPR
UFPA
UFAL
UFPR
UFPI
UFG
UFES
UFAL
UFPB
UFCG
UFES
UFPA
UFBA
UFBA
UFCG
UFPI
UFAL
UFMA
UFMA
UFG
UFES
UFG
UFPR
UFMA
UFG
UFG
UFSJ
PERIOD
3/1/2004
11/30/2004
4/1/2003
12/31/2004
5/1/2004
11/30/2004
7/1/2004
11/30/2004
3/1/2004
11/30/2004
4/1/2002
11/30/2004
6/1/2004
12/31/2004
7/1/2004
11/30/2004
3/1/2004
11/30/2004
3/1/2004
11/30/2004
3/1/2004
11/30/2004
7/1/2004
11/30/2004
7/1/2004
11/30/2004
3/1/2004
11/30/2004
5/1/2004
11/30/2004
2/1/2003
11/30/2004
7/1/2001
11/30/2004
4/1/2003
12/31/2004
3/1/2004
11/30/2004
3/1/2004
11/30/2004
4/1/2003
12/31/2004
4/1/2003
12/30/2004
4/1/2003
12/31/2004
11/1/2003
12/31/2004
8/1/2003
12/31/2004
8/30/2004
12/31/2004
4/1/2003
12/30/2004
11/1/2003
12/13/2004
4/1/2004
12/31/2004
4/1/2003
12/30/2004
8/1/2004
11/30/2004
4/1/2003
12/31/2004
9/1/2003
12/31/2004
4/1/2003
12/31/2004
6/1/2004
12/31/2004
4/1/2004
11/30/2004
4/1/2003
12/31/2004
4/1/2003
12/31/2004
5/1/2004
11/30/2004
3/1/2004
11/30/2004
3/1/2004
11/30/2004
4/1/2003
12/31/2004
2/1/2003
12/31/2004
4/1/2007
11/30/2004
GABRIEL LESSA DA SILVA LAVAGNOLI
GABRIELA ALBUQUERQUE WANDERLEY
GILBERTO DUARTE CUZZUOL
HEDMO MARCELO DOS SANTOS
HELEN CRISTINA VIEIRA FREITAS
HERMANA DE FATIMA BORGES
HIVANA NASCIMENTO SANTOS
IARA DA CUNHA RIBEIRO DA SILVA
IARA ZANDONAI DO NASCIMENTO
ÍCARO LINS LEITÃO DA CUNHA
ILNARA DA SILVA SANTOS
IVALDO PAZ NUNES
JAIRO SANTOS DA SILVA
JAQUELINE FELIX DE BRITO
JESUS OSSIAN DA CUNHA SILVA
JOABY DE SOUZA JUCÁ
JOÃO EVANGELISTA CABRAL DOS SANTOS
JOÃO PABLO PINHEIRO DA SILVA
JOÃO PAULO DOS SANTOS
JOEDSON SILVA DOS SANTOS
JOEL ALVES PEREIRA
JOSÉ ALEXANDRE R. VEIEIRA
JOSÉ CARLOS BARBOSA DE LIMA
JOSÉ EUSTÁQUIO FERREIRA
JOSÉ FABIO BOIA PORTO
JOSENALVA RODRIGUES SÁ
JUSTINO MUNIZ JUNIOR
KELINY MARTINS DE MELO SOUSA
LEOMARQUES FRANCISCO SILVA BERNARDO
LILIAN NEVES SANTA ROSA
LUCIANO MARTINS BARROS
LUZIENE MARIA DE CARVALHO LUZ
MANASSES XAVIER DE SOUZA
MANUELA CAETANO DE REZENDE FERREIRA
MANUELA DA SILVA SOUZA
MARCIA NUNES DOS SANTOS
MARCIO MIRANDA DE CARVALHO
MARCIUS PETRÚCIO DE ALMEIDA CAVALCANTE
MARCOS AURÉLIO DA SILVA CUNHA
MARLON WISNER VALGAS
MATHEUS BRIOSCHI HERKENHOFF VIEIRA
MICHEL GUERRA DE SOUZA
MICHELLY PAGANI
NATÁLIA REGINA SANTOS LOPES
NATANAILZA MARTINS ALVES
ODILON FELIPE FRANCO CAVALCANTE
PEDRO PAULO BONETTI BEAKLINI
POLIANA LUZ MOREIRA
RAFAEL DE SOUZA GROSSE
178
UFES
UFPB
UFES
UFPB
UFU
UFCG
UFBA
UFPR
UFPR
UFPB
UFPA
UFMA
UFMA
UFCG
UFPI
UFAL
UFPB
UFPR
UFG
UFPB
UFPI
UFCG
UFAL
UFU
UFAL
UFMA
UFSJ
UFPI
UFCG
UFV
UFCG
UFPI
UFPB
UFG
UFBA
UFSJ
UFPI
UFAL
UFMA
UFG
UFES
UFES
UFPR
UFMA
UFCG
UFPA
UFPR
UFV
UFPR
3/1/2004
3/1/2004
4/1/2003
2/1/2003
7/1/2004
4/1/2003
5/1/2004
7/1/2004
7/1/2004
4/1/2003
7/1/2004
5/1/2004
6/1/2004
6/1/2004
3/1/2004
8/1/2004
4/1/2004
4/1/2004
5/1/2004
3/1/2004
4/1/2003
6/1/2004
4/1/2003
7/1/2004
3/1/2004
6/1/2004
7/1/2004
3/1/2004
3/1/2004
7/1/2004
4/1/2004
3/1/2004
3/1/2004
2/1/2003
8/1/2004
7/1/2004
2/1/2003
4/1/2004
6/1/2004
4/1/2003
5/1/2004
3/1/2004
4/1/2003
6/1/2004
3/1/2004
3/1/2004
4/1/2003
7/1/2004
5/1/2004
11/30/2004
11/30/2004
12/31/2004
11/30/2004
11/30/2004
12/31/2004
11/30/2004
11/30/2004
11/30/2004
12/31/2004
12/30/2004
12/31/2004
12/31/2004
12/31/2004
11/30/2004
11/30/2004
11/30/2004
11/30/2004
11/30/2004
11/30/2004
12/31/2004
12/31/2004
12/30/2004
11/30/2004
11/30/2004
12/31/2004
11/30/2004
11/30/2004
11/30/2004
11/30/2004
11/30/2004
11/30/2004
11/30/2004
12/31/2004
11/30/2004
11/30/2004
11/30/2004
11/30/2004
12/31/2004
12/31/2004
11/30/2004
11/30/2004
12/30/2004
12/31/2004
11/30/2004
11/30/2004
12/30/2004
11/30/2004
11/30/2004
RAIMUNDO JOSÉ PINTO CUTRIM
RICARDO LUCIANO SILVEIRA PAES JUNIOR
RICK ANTONIO RISCHTER
RIVALDO DO NASCIMENTO JÚNIOR
ROBSON DE SOUZA RODRIGUES
RODRIGO ALVES DE OLIVEIRA ARRUDA
SHEILA DA SILVA FRAGOSO
SILVIA DORIA FELIX
SIMEÃO TARGINO DA SILVA
SONIA ROCHA SANTOS SOUSA
SUELLEN CRISTINA QUEIROZ ARRUDA
TERTULIANO CARREIRO DE SOUZA NETO
THYAGO DE OLIVEIRA CORDEIRO
TIAGO MOREIRA VARGAS
TIAGO RODRIGO PERDIGÃO
TURENE CAVALCANTE SOUSA
UZIEL PAULO DA SILVA
VALDEMBERG GOUVEIA DIAS
VANESSA DA SILVA ALVES
VANESSA RIBEIRO RAMOS
WAGNER SANTOS TELES DA SILVA
UFMA
UFAL
UFES
UFCG
UFG
UFPB
UFPB
UFES
UFPB
UFMA
UFPA
UFBA
UFPB
UFG
UFSJ
UFPI
UFU
UFCG
UFAL
UFBA
UFBA
179
6/1/2004
5/1/2004
4/1/2004
4/1/2003
5/1/2004
2/1/2003
5/1/2004
3/1/2004
04/01/03
5/1/2004
4/1/2004
4/1/2003
11/1/2003
5/1/2004
7/1/2004
4/1/2003
7/1/2004
6/1/2004
9/13/2004
8/1/2004
4/1/2003
12/31/2004
11/30/2004
11/30/2004
12/30/2004
31/11/2004
11/30/2004
11/30/2004
11/30/2004
12/30/2004
12/30/2004
12/31/2004
11/30/2004
10/31/2004
11/30/2004
11/30/2004
12/30/2004
11/30/2004
12/31/2004
12/30/2004
11/30/2004
12/30/2004

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