le (1h8m38s)

# Résultats de recherche

**2544**

le (1h5m50s)

## C. Matheus - Square tiled surfaces (Part 1)

a) basic definitions and examplesb) strata and genusc) reduced and primitive origamis, SL(2,R) action, Veech groupsd) automorphisms and affine homeomorphismse) homology of origamisf) Kontsevich-Zorich cocycleg) Lyapunov exponents of the Wollmilchsau Voir la vidéole (1h18m11s)

## C. Matheus - Square tiled surfaces (Part 3)

a) basic definitions and examplesb) strata and genusc) reduced and primitive origamis, SL(2,R) action, Veech groupsd) automorphisms and affine homeomorphismse) homology of origamisf) Kontsevich-Zorich cocycleg) Lyapunov exponents of the Wollmilchsau Voir la vidéole (1h3m49s)

## C. Matheus - Square tiled surfaces (Part 2)

a) basic definitions and examplesb) strata and genusc) reduced and primitive origamis, SL(2,R) action, Veech groupsd) automorphisms and affine homeomorphismse) homology of origamisf) Kontsevich-Zorich cocycleg) Lyapunov exponents of the Wollmilchsau Voir la vidéole (1h31m15s)

## B. Deroin - Monodromy of algebraic families of curves (Part 2)

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. 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 (1h8m16s)

## G. Forni - Cohomological equation and Ruelle resonnences (Part 2)

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 (1h4m44s)

## J. Aramayona - MCG and infinite MCG (Part 2)

The first part of the course will be devoted to some of the classicalresults about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston classification,abelianization, isomorphic rigidity, geometry of combinatorial models.In the second part we will explore some aspects of "big" mapping class groups, highlighting the analogies and differences with their finite-type counterparts, notably around isomorphic rigidity, abelianization, and geometry of combinatorial models. Voir la vidéole (59m19s)