Forni, Giovanni Bastien, Fanny

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 con...

Girard, Yohan Filip, Simion

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-a...

Forni, Giovanni Girard, Yohan

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 con...

Girard, Yohan Smillie, John

A major challenge in dynamics on moduli spaces is to understand the behavior of the horocycle flow. We will motivate this problem and discuss what is known and what is not known about it, focusing on the genus 2 case. Specific topics to be covered include: * SL_2(R) orbit closures and invariant measures in genus 2. * Quantitative nondivergence. * T...

Deroin, Bertrand Girard, Yohan

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. T...

Bastien, Fanny Deroin, Bertrand

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. T...

Skripchenko, Sasha Bastien, Fanny

1. Symbolic dynamics: Arnoux - Rauzy words and Rauzy gasket 2. Topology: Arnoux - Yoccoz example and its generalization 3. Novikov’s problem: how dynamics meets topology and together they help to physics 4. Lyapunov exponents for the Rauzy gasket: what do we know about them 5. Multidimensional fraction algorithms: why do they care 6. Open problem s...

Girard, Yohan Skripchenko, Sasha

1. Symbolic dynamics: Arnoux - Rauzy words and Rauzy gasket 2. Topology: Arnoux - Yoccoz example and its generalization 3. Novikov’s problem: how dynamics meets topology and together they help to physics 4. Lyapunov exponents for the Rauzy gasket: what do we know about them 5. Multidimensional fraction algorithms: why do they care 6. Open problem s...

Girard, Yohan Deroin, Bertrand

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. T...

Leininger, Christopher Bastien, Fanny

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 homeomorph...