le (59m19s)

# Résultats de recherche

**3561**

le (1h1m4s)

## B. Deroin - Monodromy of algebraic families of curves (Part 1)

The mini-course will focus on the properties of the monodromies of algebraic families of curves defined over the complex numbers. One of the goal will be to prove the irreducibility of those representations for locally varying families (Shiga). If time permit we will see how to apply this to prove the geometric Shafarevich and Mordell conjecture. The material that will be developed along the lectures are - analytic structure of Teichmüller spaces - theory of Kleinian groups - Bers embedding - b-groups - Mumford compactness criterion - Imayoshi-Shiga finiteness theorem. Voir la vidéole (1h11m15s)

## B. Deroin - Monodromy of algebraic families of curves (Part 3)

The mini-course will focus on the properties of the monodromies of algebraic families of curves defined over the complex numbers. One of the goal will be to prove the irreducibility of those representations for locally varying families (Shiga). If time permit we will see how to apply this to prove the geometric Shafarevich and Mordell conjecture. The material that will be developed along the lectures are - analytic structure of Teichmüller spaces - theory of Kleinian groups - Bers embedding - b-groups - Mumford compactness criterion - Imayoshi-Shiga finiteness theorem. Voir la vidéole (1h1m41s)

## S. Filip - K3 surfaces and Dynamics (Part 2)

K3 surfaces provide a meeting ground for geometry (algebraic, differential), arithmetic, and dynamics. I hope to discuss:- Basic definitions and examples- Geometry (algebraic, differential, etc.) of complex surfaces- Torelli theorems for K3 surfaces- Dynamics on K3s (Cantat, McMullen)- Analogies with flat surfaces- (time permitting) Integral-affine structures Voir la vidéole (1h1m18s)

## S. Filip - K3 surfaces and Dynamics (Part 3)

K3 surfaces provide a meeting ground for geometry (algebraic, differential), arithmetic, and dynamics. I hope to discuss:- Basic definitions and examples- Geometry (algebraic, differential, etc.) of complex surfaces- Torelli theorems for K3 surfaces- Dynamics on K3s (Cantat, McMullen)- Analogies with flat surfaces- (time permitting) Integral-affine structures Voir la vidéole (1h4m55s)

## G. Forni - Cohomological equation and Ruelle resonnences (Part 1)

In these lectures we summarized results on the cohomological equation for translation flows on translation surfaces (myself, Marmi, Moussa and Yoccoz, Marmi and Yoccoz) and apply these results to the asymptotic of correlations for pseudo-Anosov maps, which were recently obtained by a direct method by Faure, Gouezel and Lanneau. In this vein, we consider the generalization of this asymptotic to generic Teichmueller orbits (pseudo-Anosov maps correspond to periodic Teichmueller orbits) and to (partially hyperbolic) automorphisms of Heisenberg nilmanifolds (from results on the cohomological equation due to L. Flaminio and myself).eem Voir la vidéole (1h1m29s)

## G. Forni - Cohomological equation and Ruelle resonnences (Part 3)

In these lectures we summarized results on the cohomological equation for translation flows on translation surfaces (myself, Marmi, Moussa and Yoccoz, Marmi and Yoccoz) and apply these results to the asymptotic of correlations for pseudo-Anosov maps, which were recently obtained by a direct method by Faure, Gouezel and Lanneau. In this vein, we consider the generalization of this asymptotic to generic Teichmueller orbits (pseudo-Anosov maps correspond to periodic Teichmueller orbits) and to (partially hyperbolic) automorphisms of Heisenberg nilmanifolds (from results on the cohomological equation due to L. Flaminio and myself). Voir la vidéole (1h9m14s)

## P. Hubert - Rauzy gasket, Arnoux-Yoccoz interval exchange map, Novikov's problem (Part 1)

1. Symbolic dynamics: Arnoux - Rauzy words and Rauzy gasket2. Topology: Arnoux - Yoccoz example and its generalization3. Novikov’s problem: how dynamics meets topology and together they help to physics4. Lyapunov exponents for the Rauzy gasket: what do we know about them5. Multidimensional fraction algorithms: why do they care6. Open problem session (sometimes, say, more than 30 years open!) Voir la vidéole (1h9m14s)

## C. Leininger - Teichmüller spaces and pseudo-Anosov homeomorphism (Part 1)

I will start by describing the Teichmuller space of a surface of finite type from the perspective of both hyperbolic and complex structures and the action of the mapping class group on it. Then I will describe Thurston's compactification of Teichmuller space, and state his classification theorem. After that, I will focus on pseudo-Anosov homeomorphisms, describe a little bit about their dynamics, and discuss the geometry/dynamics of the associated mapping tori. Voir la vidéole (1h8m38s)