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Escola de Verão do Instituto de Matemática da UFRJ - 2009

Cursos de Nivelamento

Horário: 3ª de 14h às 16h, 4ª e 5ª de 10h às 12h 
Sala: D-210a 
Professor: Jorge Achcar

Horário: 2ª, 4ª e 6ª de 10h às 12h
Sala: D-116
Professor: Glauco Valle

Cursos de Mestrado e Doutorado

Dias e horários: 09/08 - 14h30 e 16h00
Sala: sala C116
Temas: 

às 14h30 Joel Angel Cisneros Gómez (UFF)
Folheações fortes mínimais em produtos tortos de sistemas iterados de funções
Estudamos produtos tortos localmente constantes sobre shifts de finitos símbolos, com um espaço métrico compacto como a fibra. Introduzimos um novo critério para determinar a densidade das folhas da folheação forte instável (e forte estável), ou seja, para sua minimalidade. Quando a fibra é um círculo, mostramos que ambas folheações fortes são mínimais para um conjunto aberto e denso de skew-product robustamente transitivos. Apresentamos exemplos em que uma folheação é mínimal ou nenhuma é mínimal. Nossa abordagem envolve a investigação da dinâmica do Sistema Iterado de Funções (ou simplesmente IFS nas siglas em Inglês). 
 
às 16h00 Dominique Malicet (Université Gustave Eiffel)
Spectral properties and limit theorems for (mostly) contracting random dynamical systems
In 1982, Le Page deeply studied the asymptotic behavior of random products of matrices through the spectral properties of the transfer operator of the action on the projective space. More precisely, under few assumptions, he proved that the operator satisfies a property called spectral gap, and he deduces various limit theorems (central limit theorem and large deviation theorem among others) by using the so-called Nagaev method. In a work with Pablo G. Barrientos we prove that an analog spectral property and its consequences hold for any random dynamical system on a  compact metric space satisfying some contraction property, which may be expressed in terms of Lyapunov exponents. In particular, it applies to random compositions of diffeomorphisms of the circle under very few assumptions.

Dias e horários: Terças e Quintas, 10 hs às 12 hs.
Sala: B-106b
Professores: Regis Castijos e Alexander Arbieto
Ementa: Conservatividade, Ergodicidade, Operador dual, Transformações induzidas, Mixing, K-automorfismo infinito, Entropia.
Referências:
1. J. Aaronson, "An Introduction to the Infinite Ergodic Theory", Mathematical Surveys and Monographs volume 50, AMS, 1997,
2. U. Krengel, Entropy of conservative transformations, Z. Wahrscheinlichkeitstheorie verw. Geb. 7 (1967), 161-181.
3. U. Krengel and L. Sucheston, On mixing in infinite measure spaces, Z. Wahrscheinlichkeitstheorie verw. Geb. 13 (1969), 150-164.
4. W. Parry, Ergodic and spectral analysis of certain infinite measure preserving transformations, Proc. of the AMS, 16 no 5 (1965), 960-966.
5. Ya. B. Pesin. Characteristic Lyapunov exponents and smooth ergodic theory, Russian Math. Surveys 32 no 4 (1977), 55-114.

Sala: B-106b 
Professor: Alexander Arbieto

Horário: 2ª, 4ª e 6ª de 10h às 12h
Sala: B-106a 
Professor: Didier Jaques François Pilod

Palestras Programadas

Angel Cano, UNAM
Anthony Davison, EPFL
Edgar Goodaire, Memorial University of Newfoundland
Federico Rodriguez Hertz, IMERL
Marc Genton, Texas A&M University
Peter Green, University of Bristol
Sudarshan Sehgal, University of Alberta

Jorge Achcar, USP-Ribeirão Preto
Cristian Colleti. Universidade Federal do ABC
Krerley Oliveira. UFAL
Valentin Sisko, UFF

Dia: 06/03
Horário: 15h
Sala: C-116
Resumo: Climatic change is forecast to change the frequency and sizes of extreme events such as major storms, heatwaves and the like, and the effects
on human mortality, health and infrastructure are starting to become of major concern to public health authorities, engineers, and other planners. Predicting the possible impacts of such events necessarily entails extrapolation outside the range of the available data, and the usual basis for this is the statistics of extremes and its underlying probability models. Analysis of extreme events for single series of data is now well-established and used in a variety of disciplines, from hydrology through metallurgy to finance and insurance, but the corresponding theory for events in space is underdeveloped. After some motivating material, this talk will describe the basic probabilistic theory of extremes, and then will outline how it may be extended to the spatial context, before turning to more statistical matters such as fitting of appropriate models to data and their use for prediction of future events.

Dia: 06/03
Horário: 16h
Sala: C-116
Resumo: We present a general framework for Bayesian model-based clustering, in which subset labels are exchangeable, and items are also  xchangeable, possibly up to covariate effects. It is rich enough to encompass a variety of existing procedures, including some recently discussed methodologies involving stochastic search or hierarchical clustering, but more importantly allows the formulation of clustering procedures that are optimal with respect to a specified loss function. Our focus is on loss functions based on pairwise coincidences, that is, whether pairs of items are clustered into the same subset or not. We go on to discuss a Bayesian mixture model that allows us to express a gene expression profile across different experimental conditions as a linear combination of covariates characterising those conditions, plus error. In a standard Bayesian nonparametric formulation, the regression coefficients of the linear combination and the error precisions would jointly follow a Dirichlet process (DP). In this set-up the clusters generated by the process are a priori exchangeable. However in the gene expression context, it commonly occurs that some genes are not influenced by the covariates, but fall into a `background' class. This calls for an extension to the DP model generating a background cluster that is not exchangeable with the others. This is joint work with Dr John Lau, now at University of Western Australia

Dia: 10/02 
Horário: 14h 

Minicursos Avançados

Professor: Federico Rodriguez Hertz

Professor: Krerley Oliveira
Topo