Report Im-Agimb

I N D E X

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, 6th 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

3 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

4 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

5 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

6 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

7 Millennium Institute Global and Integrated Advancement of Mathematics in Brazil – IM-AGIMB

Report of Activities - Summaries

Areas

Mathematical Instruction and Olympiads

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

8 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.

Weather Prediction and Climate

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. IM- AGIMB 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

9 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.

10 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.

Mathematical Modeling of Biological Systems and of Linguistics

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 micro- organism 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.

11 Differential Geometry

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. IM- AGIMB 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.

Algebra and Algebraic Geometry

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

12 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.

Partial Differential Equations

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 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, 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.

Cooperation with Latin America

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 Post- Doctoral 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

16 number of CNPq’s Scientific Initiation fellowhips have been provided to them via IM- AGIMB. 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 Millennium Institute Global and Integrated Advancement of Mathematics in Brazil – IM-AGIMB

Reports

Areas of Activities

Mathematical Instruction and Olympiads

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 Schools Students V Olimpíada de Matemática UNIVATES 102 2.960 III Olimpíada Metropolitana de Matemática 30 460 Olimpíada de Matemática - Fase Regional Bahia 2002 167 3.000 XV Olimpíada Campinense de Matemática 60 2.510 V Olimpíada Regional de Matemática de Santa Catarina 40 1.000 Olimpíada Paulista de Matemática 2002 900 35.000 Olimpíada Regional de Matemática Grande Porto Alegre 20 1.200 2002 XI Olimpíada de Matemática do Estado de Goiás 500 1.800 Olimpíada Capixaba de Matemática 2002 267 17.792 Olimpíada Paraense de Matemática 2002 20 2.500 Olimpíada de Matemática do Estado do Rio de Janeiro 2002 230 3.000 II Olimpíada Piauiense de Matemática 25 1.049 Olimpíada Mineira de Matemática 2002 350 4.000

18 Olimpíada Pessoense de Matemática 35 350 XIII Olimpíada de Matemática do Rio Grande do Norte 30 1.500 Olimpíada Cearense de Matemática 2002 20 2.500 Total 2.796 83.417

Incentive to the Regional Olympiads in Brazil in 2003 18 Regional Olympiads took place in Brazil, with the participation of 2.928 schools and a total of 108,390 students of elementary and high schools. Regional Olympiads Schools Students I Olimpíada Alagoana de Matemática 19 490 VI Olimpíada de Matemática UNIVATES 68 5.556 IV Olimpíada Metropolitana de Matemática 41 550 Olimpíada de Matemática - Fase Regional Bahia 2003 167 2.830 XVI Olimpíada Campinense de Matemática 204 3.000 VI Olimpíada Regional de Matemática de Santa Catarina 102 5.074 Olimpíada Paulista de Matemática 2003 1100 45.000 Olimpíada Pernambucana de Matemática "Ruy 40 2.400 Luís Gomes" 2003 Olimpíada Regional de Matemática Grande Porto Alegre 60 2.400 2003 XII Olimpíada de Matemática do Estado de Goiás 573 2.400 Olimpíada Capixaba de Matemática 2003 312 20.944 Olimpíada Paraense de Matemática 2003 17 1.500 Olimpíada de Matemática do Estado do RJ 2003 30 200 III Olimpíada Piauiense de Matemática 30 1.850 Olimpíada Mineira de Matemática 2003 70 4.055 Olimpíada Pessoense de Matemática 20 1.500 XIV Olimpíada de Matemática do Rio Grande do Norte 35 1.791 Olimpíada Cearense de Matemática 2003 40 6.850 Total 2.928 108.390

Incentive to the Regional Olympiads in Brazil in 2004 20 Regional Olympiads took place in Brazil, with the participation of 3.849 schools and a total of 131,676 students of elementary and high schools. Regional Olympiads Schools Students II Olimpíada Alagoana de Matemática 25 600 VII Olimpíada de Matemática UNIVATES 100 6.820 V Olimpíada Metropolitana de Matemática 70 600 Olimpíada de Matemática - Fase Regional Bahia 2003 300 5.000 XVII Olimpíada Campinense de Matemática 60 2.500 VII Olimpíada Regional de Matemática de Santa Catarina 126 4.000 Olimpíada Paulista de Matemática 2003 1.500 60.000 Olimpíada Pernambucana de Matemática "Ruy Luís Gomes" 110 5.500 2003 Olimpíada Regional de Matemática Grande Porto Alegre 80 3.000 2003 XIII Olimpíada de Matemática do Estado de Goiás 300 3.000 Olimpíada Paraense de Matemática 2003 17 1.956 IV Olimpíada Piauiense de Matemática 48 2.500 Olimpíada Mineira de Matemática 2004 450 4.500 Olimpíada Pessoense de Matemática 35 1.500 Olimpíada Cearense de Matemática - 2003 180 20.000

19 Olimpíada de Matemática da Região do ABC 20 200 Olimpíada de Matemática de Rio Preto 32 1.500 Olimpíada Regional de Matemática do Litoral Norte do Rio 115 2.500 Grande do Sul Olimpíada Regional de Matemática da Unochapecó 81 4.000 Olimpíadas Sergipanas de Matemática 200 2.000 Total 3.849 131.676

International Olympiads The participation of Brazil at the International Mathematical Olympiads has grown exponentially, including the International Olympiad, the Ibero-American Olympiad, Cone- Sul, 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 Weather Prediction and Climate

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 biome- climate 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 (20- 60 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 Technion- Haifa (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, 435- 446, 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.105- 112, 2002. 20. E. F. Costa and J. B. R. do Val. On the Observability and Detectability of Continuous- Time Markov Jump Linear Systems, SIAM J. on Control & Optimization, 41, 1295- 1314, 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 Mean- Semivaraince 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 time- reversible 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: f- Structures 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 reversibility- na 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, Stochastic versions of Hartman-Grobman theorems, Stochastics and Dynamics.

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 Non- Linear 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 sub- Riemannian 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 co- authorships 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 BBW- logic. 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 quasi- Newton 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 non- coercive 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, 631- 650, 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, 151- 165, 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, 3851- 3859, 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, 127- 133, 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, 307- 318, 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-rigid- body 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 and Morse inequalities.Transactions of the American Mathematical Society. 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), 171- 180, 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 and Luiz Velho, Fundamentos da Computação Gráfica. IMPA, 2003. 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 L ucena 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, IMPA. Advisor: Luiz Velho and Luiz Henrique Figueiredo. 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 Mathematical Modeling of Biological Systems and of Linguistics

PART I – Biological systems 1. Conceptual summary of the advances during the last 30 months. 2. List of publications during the last 30 months. 3. List of completed doctorates during the last 30 months. 4. 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. Introduction 2. Conceptual achievements in the are in the last 30 months. 3. Scientific Production 4. Nurturing of human resources in the period 5. Contribution by the IM-AGIMB 6. 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 quasi- species 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 high- frequency 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), 709- 723, 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. J. Hofbauer (Vienna) 2. Michael Turelli (UCD) 3. Karl Sigmund (Vienna) 4. Peter Markowich (Vienna) 5. Martin Nowak (Harvard) 6. Franziska Michor (Harvard) 7. Christoph Hauert (UBC) 8. Larry Liebovitch (F.A.U.) 9. Greg Huber (UMB) 10. 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 intra- cellular 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 cut- points, 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 Differential Geometry

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, sub- Riemannian 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.

Scientific Publications 2002-2004 1. Borrelli, Gorodsky, C., Minimal Legendrian submanifolds and absolutely area- minimizing cones, Diff. Geom and Applic, 2004. 2. Do Carmo, M. P., Elbert, M. F., On stable complete hypersurfaces with vanishing r- mean 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 r- Mean 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, 465- 488, 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 semi- Riemannian 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 R3. 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 3- Spaces 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. ij 57. Pina, R., Tenenblat, K., On metrics satisfying equation R-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 R5, 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 3- manifolds, 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 Algebra and Algebraic Geometry

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 2- grups 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 Scientific Publications 2002-2004 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, 267- 285, 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 non- existence 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.

77 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 2- manifolds, 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 Â2, Journal of Differential Equations, 2004. 10. C. Gutierrez, A. Fernandes and R. Rabanal, On local diffeomorphisms of Ân 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, C1 robust singular transitive sets for three- dimensional 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 Henon- like attractors, Annals de l´Institut 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 time- reversible 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 R3, 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.

Scientific Production - 2003 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 C1- flows, 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, 135- 146, 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 non- nuls pour des produits déterministes de matrices, Ann. Inst. Henri Poincaré, An. Non- Linéaire, 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, 735- 745, 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 ³ 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. 43. F. Abdenur, A. Avila and J. Bochi, Robust transitivity and topological mixing for C1 flows, Procs. Amer.Math. Soc, 2003. 44. F. Abdenur, Attractors of generic diffeomorphisms are persistent, Nonlinearity, 1, 301- 311, 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 R4, 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, Ergodic Theory and Dynamical Systems, 2003.

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.

Scientific Production - 2002 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 non- nuls 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.

87 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, Ergodic Theory and Dynamical Systems, 2002. 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. 30. F. Abdenur, A. Avila and J. Bochi, Robust transitivity and topological mixing for C1 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.

88 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.

89 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

Human Resources - 2003 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 Rn e C2. 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

90 11. Mychelle Dysman. Doutor. “Hausdor dimension of repellers of maps with holes. Marcelo Viana 12. Rafael Souza. Doutor. Subações de sistemas um-dimensionais fracamente hiperbólicos. Artur Lopes 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

Human Resources - 2002 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 C1 generic systems. Marcelo Viana 6. German Aubin Arroyo. Doutor. Homoclinic bifurcations and uniform hyperbolicity for 3- dimensional 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

91 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.

Cooperation with Latin America 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.

92 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.

93 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 Sigman-p+1-germs from Rn to Rp, n ³ 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 multi- germs over R and C, Compositio Mathematica, 131, 121-160, 2002. 5. J.W. Bruce and F. Tari, Families of surfaces in R4, Proc. Edinb. Math. Soc., 45(2), 181- 203, 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

94 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 IM- AGIMB 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 IM- AGIMB 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 Ibilce- Unesp/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.

96 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, PUC- Rio, 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), 275- 291, 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, 115- 130, 2003. 18. D.L. Gonçalves and M. Golasinski, Spherical space forms -homotopy types and self- equivalences. 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), 1223- 1245, 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, 553- 567, 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(1- 2), 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 (1960- 1999). 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 2- manifolds, 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), 3111- 3115, 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, Proyecciones- Revista 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 3- manifolds with an application to circle foliations, Mathematische Annalen, 322(3), 493- 524, 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. 2 6. Daciberg L. Gonçalves John Guaschi, The braid group Bm,n(S ) 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 Theory- Elsevier, 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: 3035- 3045, 2004. 3. D. Levcovitz, V.H. Jorge Perez, M.J. Saia, Invariants, equisingularity and Euler obstructions of map-germs from Cn to Cn, 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 R2, 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 Sigman-p+1-germs from Rn to Rp, 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, 813- 821, 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 bi- Lipschitz 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 non- singular embeddings of surfaces in R5. 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 Rn, Bulletin of the Belgian Mathematical Society, 2003.

103 33. S.M. Moares, M.C. Romero-Fuster, Semiumbilics and Normal Fields on Surfaces Immersed in Rn, 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 multi- germs 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, PUC- Rio, 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:

106 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), Marie- France 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 2- connected 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 co- authors 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. Wakabayashi, Multidimensional cube packing, Algorithmica, 40(3), 173-187, 2004. 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, 281- 292, 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), 161- 177, 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 1- join 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 clique- independent 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 Cn 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 pseudo- aleatórios 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. Supervisor: J. Meidanis (IC-UNICAMP), 2002.

112 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 Partial Differential Equations

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 ``Escola'' 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.

Publications 2002-2004 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 Water- Saturated 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), 1- 2, 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), 905- 922, 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 single- phase 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), 251- 280, 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 Zakharov- Kuznetsov 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, 48- 83, 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 Zakharov- Kuznetsov 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 transport- dominated 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.

130 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 Water- Saturated 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, 48- 83, 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)

132 Cooperation with Latin America

· 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 Post- Doctoral 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 Millennium Institute Global and Integrated Advancement of Mathematics in Brazil – IM-AGIMB

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 IM- AGIMB. 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 Publications 2002-2004 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

Publications 2002-2004 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.

Scientific Initiation 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

Differential Geometry 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 § Differential Geometry 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 L´Academie 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 L´Institut 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 Publications 2002-2004 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, 508- 521, 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 Two- Phase 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)

Publications 2002-2004 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), 359- 375, 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 C1- maps of the real plane. Canadian Journal of Mathematics. Inglaterra, 54(6), 1187- 1201, 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. 16. Munaro, Celso José, Rosado Filho, M., Borges, R.M., Munareto, S.S., Costa, W.T., 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. 17. Munaro, Celso José, Rosado Filho, M., Borges, R.M., Munareto, S.S., Costa, W.T., 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.

151 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. · 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: · 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: · 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.

152 Impacto do IM-AGIMB A execução do projeto trouxe até o presente os seguintes impactos positivos nas atividades docentes no IME/UFG. · 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

153 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: · 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. As linhas de pesquisa são: · 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. As linhas de pesquisa são: · 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.

154 As linhas de pesquisa são: · 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. As linhas de pesquisa são: · 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. As linhas de pesquisa são: · 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 R3, 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.

155 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 Kgij =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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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 a equacao da onda, Atas do encontro regional da SBPC, 24ª, 2004.

157 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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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.

Scientific Initiation 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.

159 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

Publications 2002-2004

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.

160 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 Mathematical Analysis and Applications, 275, 789-803, 2002. 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 Institution Date João Marcos Bezerra do Ó USACH/Chile 2002 João Marcos Bezerra do Ó UNICAMP 2002, 2003, 2004. João Marcos Bezerra do Ó UnB 2003, 2004. João Marcos Bezerra do Ó UFC 2003, 2004. João Marcos Bezerra do Ó UFCG 2002; 2003, 2004 Everaldo Souto de Medeiros UFCG 2002; 2003; 2004 Everaldo Souto de Medeiros UNICAMP 2004 Everaldo Souto de Medeiros UFMG 2003 Everaldo Souto de Medeiros IMPA 2004 Pedro Hinojosa UFC 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 Non- Cilindrical 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 R2, 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 ÂN, 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 ÂN. 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 ÂN. 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 Mathematical Analysis and Applications, 265, 103-127, 2002. 35. Bertone, A.M.A., Abreu, J.V.G., Discontinuous Elliptic Problems in ÂN 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.

Scientific Initiation 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 · Partial Differential Equations · Fuzzy Topology · Operational Research

Publications 2002-2004 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, 244- 251, 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 Piauí and Maranhão. We have supervised mostly teachers from the rural areas:

ANO / SEMESTRE TOTAL 2002/2 50 2003/1 72 2003/2 96 2004/1 140 2004/2 170

We would like to propose that this training program could evolve to a M.Sc. program, tied to incentives such as better salaries.

Publications 2002-2004 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. Luiz Cláudio Pereira, UFV, Doutor UNB 1998, Applied Mathematics 2. Margareth da Silva Alves, UFV, Doutor, UFRJ, 1994, Analysis/EDP 3. Marinês Guerreiro, UFV, PhD, Univ. Manchester 1997, Algebra 4. Sandro Vieira Romero, UFV, Doutor IME-USP 2001, Applied Mathematics 5. Simone Maria de Moraes, UFV, Doutor UNICAMP, 2002, Geometry and Topology 6. Cícero Fernandes de Carvalho, UFU, Doutor IMPA 1994, Pos-Doc Harvard University 1998, Algebraic Geometry 7. Geraldo Márcio de Azevedo Botelho, UFU, Doutor UNICAMP 1995, Analysis 8. Jocelino Sato, UFU, Doutor, UFCe, 2000, Geometry 9. Márcio José Horta Dantas, UFU, Doutor UFRJ 1988- Applied Mathematic 10. Walter dos Santos Motta Junior, UFU, Doutor ICMSC-USP 1992, Topology 11. Francinildo Nobre Ferreira, UFSJ, Doutor UNB 1999, Geometry 12. Mário Dávila, UFSJ, Doutor UFRJ 1995, Analysis/EDP 13. Adilson Vieira Brandão, UFOP, Doutor, UNICAMP 1998, Analysis/Optimization 14. Antônio Luis Rosa, UFOP, Doutor, USP 2000, Algebra 15. Felipe Rogério Pimentel, UFOP, Doutor, UNICAMP 2003, Applied Mathematic 16. Gonçalo Astorga Tapia, UFOP, Doutor, USP 2003, Analysis 17. João Luís Martins, UFOP, Doutor, UNICAMP 2000, Applied Mathematic/Geophysic 18. 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).

Scientific Initiation We obtained 12 fellowships. The projects are described in detail in our full report.

Publications 2002-2004

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, 555- 568, 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 N- functions, 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. 9. F.M. Forger, E.S.V. Romero, Covariant Poisson Brackets in Geometric Field Theory, Communications in Mathematical Physics, 2004. 10. Alves, C.O., Carriao, P.C., Miyagaki, O.H., Existence of homoclinic orbits for asymptotically periodic systems involving Duffing like equations, Applied Mathematics Letters, 16, 639-642, 2003. 11. Alves, C.O., Carriao, 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, Birkhauser-Berlim, 54, 225-238, 2003. 12. Alves, C.O., Bezerra, J.M., Miyagaki, O.H., On a class of singular biharmonic problems involving critical exponents, Journal of Mathematical Analysis and Applications, 277(1), 12-26, 2003.

174 13. Dantas, M.J.H., Balthazar, J.M., On the appearence of a Hopf bifurcation in a non-ideal mechanical problem, Mechanics Research Communications, 30, 493-503, 2003. 14. Guerreiro, M., Grishkov, A.N., Simple classical Lie Algebras in characteristic 2 and their gradations I, International Journal of Mathematics Game Theory and Algebra, New York, 13(3), 239-252, 2003. 15. Guerreiro, M., Grishkov, A.N., Simple classical Lie Algebras in characteristic 2 and their gradations II, International Journal of Mathematics Games Theory and Algebra, New York, 14(13), 1-15, 2003. 16. Magalhães, P.M.D., Coaylateran, Edson Alberto, Weak Solutions for Stochastic FitzHugh-Nagumo Equations..Stochastic Analysis and Applications, 21(2), 443-463, 2003. 17. Carvalho, C., Torres, F., On numerical semigroups related to coverings of curves. Semigroup Forum., New York, 67(2), 344-354, 2003. 18. Moraes, S.M., Romero-Fuster, M.C., Semiumbilics and Normal Fields on Surfaces Immersed in Ân, n>3, Rocky Mountain Journal of Maths, 2003. 19. Carvalho, C., Weierstrass Gaps and Curves on a Scroll. Beitrage R Algebra Geom., Alemanha, 43(1), 209-216, 2002. 20. Carrião, P.C., Miyagaki, O.H., Existence of nontrivial solutions of elliptic variational systems in unbounded domains, J. of Nonlinear An. Theory Methods and Applications, 51(1), 155-169, 2002. 21. Alves, C.O., Carriao, P. C., Miyagaki, O.H., On the existence of positive solutions of a perturbed Hamiltonian systems in Ân. Journal of Mathematical Analysis and Applications, 276, 673-690, 2002. 22. Sato, J., Stability of O(p+1) × O(p+1)-Invariant Hypersurfaces with Zero Scalar Curvature in Euclidean Space. Annals of Global Analysis and Geometry, 22(2), 135- 155, 2002. 23. Botelho, G.M.A., Weakly compact and absolutely summing polynomials. Journal of Mathematical Analysis and Applications, 265, 458-462, 2002.

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 UNESP 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

176 Scientific Initiation Fellowships

NAME INSTITUTION PERIOD AILTON RIBEIRO DE ASSIS UFPB 3/1/2004 11/30/2004 ALCIDIA DUTRA LOPES UFPA 4/1/2003 12/31/2004 ALENE ALCANTARA REIS UFBA 5/1/2004 11/30/2004 ALESSANDRA LEITE BATISTA UFPR 7/1/2004 11/30/2004 ALESSANDRO GAIO CHIMENTON UFPR 3/1/2004 11/30/2004 AMANDA SILVA MARQUES VILARINS UFAL 4/1/2002 11/30/2004 ANA CRISTINA BITTENCOURT DE JESUS UFBA 6/1/2004 12/31/2004 ANA RITA CAETANO BOCHINI UFSJ 7/1/2004 11/30/2004 ANDERSON CARVALHO DOS SANTOS UFAL 3/1/2004 11/30/2004 ANDERSON DAVID DE SOUZA CAMPELO UFPA 3/1/2004 11/30/2004 ANDERSON LUIS ALBUQUERQUE DE ARAUJO UFPA 3/1/2004 11/30/2004 ANTONIO PEREIRA DE FARIAS FILHO UFPB 7/1/2004 11/30/2004 ARIANE PIOVEZAM ENTRINGER UFV 7/1/2004 11/30/2004 ARISTÓTELES MAURÍCIO PEREIRA DOS SANTOS UFPI 3/1/2004 11/30/2004 AURELIO SOARES DE CARVALHO UFES 5/1/2004 11/30/2004 BARBARA COSTA DA SILVA UFBA 2/1/2003 11/30/2004 BRICELA DE ARRUDA FRANCHINI UFV 7/1/2001 11/30/2004 BRUNO MENDONÇA REY DOS SANTOS UFPR 4/1/2003 12/31/2004 CARLA CRISTINA DE SOUZA TAVARES UFPA 3/1/2004 11/30/2004 CARLOS ALBERTO SILVA DOS SANTOS UFAL 3/1/2004 11/30/2004 CAROLINE ELISA MURR UFPR 4/1/2003 12/31/2004 CRISTIANY DE MOURA BARROS UFPI 4/1/2003 12/30/2004 DANIEL MENDES AZERÊDO UFG 4/1/2003 12/31/2004 DANÚBIA JUNCA UFES 11/1/2003 12/31/2004 DAVI ALISSON DOS SANTOS NOBREGA UFAL 8/1/2003 12/31/2004 DIOGO DE SANTANA GERMANO UFPB 8/30/2004 12/31/2004 DIOGO DINIZ PEREIRA DA SILVA E SILVA UFCG 4/1/2003 12/30/2004 DOUGAS ARAUJO VICTOR UFES 11/1/2003 12/13/2004 DOUGLAS DE OLIVEIRA MAIA UFPA 4/1/2004 12/31/2004 EDNALDO OLIVEIRA DA SILVA JUNIOR UFBA 4/1/2003 12/30/2004 ELIANE DA SILVA DOS SANTOS UFBA 8/1/2004 11/30/2004 EMERSON SOUZA SILVA UFCG 4/1/2003 12/31/2004 ENNE KAROL VENANCIO DE SOUSA UFPI 9/1/2003 12/31/2004 ERIKSON ALEXANDRE FONSECA DOS SANTOS UFAL 4/1/2003 12/31/2004 EUGÊNIO MENDES M. FILHO UFMA 6/1/2004 12/31/2004 EVALDO DE ALMEIDA ALBUQUERQUE UFMA 4/1/2004 11/30/2004 FABIANA CHAGAS UFG 4/1/2003 12/31/2004 FABIO LUIZ BORGES SIMAS UFES 4/1/2003 12/31/2004 FANG CHOU LEE UFG 5/1/2004 11/30/2004 FERNANDA MOCELIN SCHENA UFPR 3/1/2004 11/30/2004 FLANK DAVID MORAIS BEZERRA UFMA 3/1/2004 11/30/2004 FLÁVIA FERREIRA RAMOS UFG 4/1/2003 12/31/2004 FRANCIANE JOSE DA SILVA UFG 2/1/2003 12/31/2004 FRANCISNMARA FERNANDES GUERRA SILVA UFSJ 4/1/2007 11/30/2004

177 GABRIEL LESSA DA SILVA LAVAGNOLI UFES 3/1/2004 11/30/2004 GABRIELA ALBUQUERQUE WANDERLEY UFPB 3/1/2004 11/30/2004 GILBERTO DUARTE CUZZUOL UFES 4/1/2003 12/31/2004 HEDMO MARCELO DOS SANTOS UFPB 2/1/2003 11/30/2004 HELEN CRISTINA VIEIRA FREITAS UFU 7/1/2004 11/30/2004 HERMANA DE FATIMA BORGES UFCG 4/1/2003 12/31/2004 HIVANA NASCIMENTO SANTOS UFBA 5/1/2004 11/30/2004 IARA DA CUNHA RIBEIRO DA SILVA UFPR 7/1/2004 11/30/2004 IARA ZANDONAI DO NASCIMENTO UFPR 7/1/2004 11/30/2004 ÍCARO LINS LEITÃO DA CUNHA UFPB 4/1/2003 12/31/2004 ILNARA DA SILVA SANTOS UFPA 7/1/2004 12/30/2004 IVALDO PAZ NUNES UFMA 5/1/2004 12/31/2004 JAIRO SANTOS DA SILVA UFMA 6/1/2004 12/31/2004 JAQUELINE FELIX DE BRITO UFCG 6/1/2004 12/31/2004 JESUS OSSIAN DA CUNHA SILVA UFPI 3/1/2004 11/30/2004 JOABY DE SOUZA JUCÁ UFAL 8/1/2004 11/30/2004 JOÃO EVANGELISTA CABRAL DOS SANTOS UFPB 4/1/2004 11/30/2004 JOÃO PABLO PINHEIRO DA SILVA UFPR 4/1/2004 11/30/2004 JOÃO PAULO DOS SANTOS UFG 5/1/2004 11/30/2004 JOEDSON SILVA DOS SANTOS UFPB 3/1/2004 11/30/2004 JOEL ALVES PEREIRA UFPI 4/1/2003 12/31/2004 JOSÉ ALEXANDRE R. VEIEIRA UFCG 6/1/2004 12/31/2004 JOSÉ CARLOS BARBOSA DE LIMA UFAL 4/1/2003 12/30/2004 JOSÉ EUSTÁQUIO FERREIRA UFU 7/1/2004 11/30/2004 JOSÉ FABIO BOIA PORTO UFAL 3/1/2004 11/30/2004 JOSENALVA RODRIGUES SÁ UFMA 6/1/2004 12/31/2004 JUSTINO MUNIZ JUNIOR UFSJ 7/1/2004 11/30/2004 KELINY MARTINS DE MELO SOUSA UFPI 3/1/2004 11/30/2004 LEOMARQUES FRANCISCO SILVA BERNARDO UFCG 3/1/2004 11/30/2004 LILIAN NEVES SANTA ROSA UFV 7/1/2004 11/30/2004 LUCIANO MARTINS BARROS UFCG 4/1/2004 11/30/2004 LUZIENE MARIA DE CARVALHO LUZ UFPI 3/1/2004 11/30/2004 MANASSES XAVIER DE SOUZA UFPB 3/1/2004 11/30/2004 MANUELA CAETANO DE REZENDE FERREIRA UFG 2/1/2003 12/31/2004 MANUELA DA SILVA SOUZA UFBA 8/1/2004 11/30/2004 MARCIA NUNES DOS SANTOS UFSJ 7/1/2004 11/30/2004 MARCIO MIRANDA DE CARVALHO UFPI 2/1/2003 11/30/2004 MARCIUS PETRÚCIO DE ALMEIDA CAVALCANTE UFAL 4/1/2004 11/30/2004 MARCOS AURÉLIO DA SILVA CUNHA UFMA 6/1/2004 12/31/2004 MARLON WISNER VALGAS UFG 4/1/2003 12/31/2004 MATHEUS BRIOSCHI HERKENHOFF VIEIRA UFES 5/1/2004 11/30/2004 MICHEL GUERRA DE SOUZA UFES 3/1/2004 11/30/2004 MICHELLY PAGANI UFPR 4/1/2003 12/30/2004 NATÁLIA REGINA SANTOS LOPES UFMA 6/1/2004 12/31/2004 NATANAILZA MARTINS ALVES UFCG 3/1/2004 11/30/2004 ODILON FELIPE FRANCO CAVALCANTE UFPA 3/1/2004 11/30/2004 PEDRO PAULO BONETTI BEAKLINI UFPR 4/1/2003 12/30/2004 POLIANA LUZ MOREIRA UFV 7/1/2004 11/30/2004 RAFAEL DE SOUZA GROSSE UFPR 5/1/2004 11/30/2004

178 RAIMUNDO JOSÉ PINTO CUTRIM UFMA 6/1/2004 12/31/2004 RICARDO LUCIANO SILVEIRA PAES JUNIOR UFAL 5/1/2004 11/30/2004 RICK ANTONIO RISCHTER UFES 4/1/2004 11/30/2004 RIVALDO DO NASCIMENTO JÚNIOR UFCG 4/1/2003 12/30/2004 ROBSON DE SOUZA RODRIGUES UFG 5/1/2004 31/11/2004 RODRIGO ALVES DE OLIVEIRA ARRUDA UFPB 2/1/2003 11/30/2004 SHEILA DA SILVA FRAGOSO UFPB 5/1/2004 11/30/2004 SILVIA DORIA FELIX UFES 3/1/2004 11/30/2004 SIMEÃO TARGINO DA SILVA UFPB 04/01/03 12/30/2004 SONIA ROCHA SANTOS SOUSA UFMA 5/1/2004 12/30/2004 SUELLEN CRISTINA QUEIROZ ARRUDA UFPA 4/1/2004 12/31/2004 TERTULIANO CARREIRO DE SOUZA NETO UFBA 4/1/2003 11/30/2004 THYAGO DE OLIVEIRA CORDEIRO UFPB 11/1/2003 10/31/2004 TIAGO MOREIRA VARGAS UFG 5/1/2004 11/30/2004 TIAGO RODRIGO PERDIGÃO UFSJ 7/1/2004 11/30/2004 TURENE CAVALCANTE SOUSA UFPI 4/1/2003 12/30/2004 UZIEL PAULO DA SILVA UFU 7/1/2004 11/30/2004 VALDEMBERG GOUVEIA DIAS UFCG 6/1/2004 12/31/2004 VANESSA DA SILVA ALVES UFAL 9/13/2004 12/30/2004 VANESSA RIBEIRO RAMOS UFBA 8/1/2004 11/30/2004 WAGNER SANTOS TELES DA SILVA UFBA 4/1/2003 12/30/2004

179