2018

In  the  first two lectures I will try to tell (or, rather, to  give  an  idea)  of  how  Maryam Mirzakhani has counted simple  closed  geodesics on hyperbolic surfaces. I plan to briefly  mention her

In  the  first two lectures I will try to tell (or, rather, to  give  an  idea)  of  how  Maryam Mirzakhani has counted simple  closed  geodesics on hyperbolic surfaces. I plan to briefly  mention her

Multicurves have played a fundamental role in the study of mapping class groups of surfaces since the work of Dehn. A beautiful method of describing such systems on the n-punctured disk is given by

We will give the proof of Mirzakhani's theorem that the earthquake flow and Teichmuller unipotent flow are measurably isomorphic. We will assume some familiarity with quadratic differentials, but no

We will give the proof of Mirzakhani's theorem that the earthquake flow and Teichmuller unipotent flow are measurably isomorphic. We will assume some familiarity with quadratic differentials, but no

We will give the proof of Mirzakhani's theorem that the earthquake flow and Teichmuller unipotent flow are measurably isomorphic. We will assume some familiarity with quadratic differentials, but no

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

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

Singular euclidean structures on surfaces are a key tool in the study of the mapping class group, of Teichmüller space, and of kleinian three-manifolds.  François Guéritaud, while studying work of Ian

a) basic definitions and examples b) strata and genus c) reduced and primitive origamis, SL(2,R) action, Veech groups d) automorphisms and affine homeomorphisms e) homology of origamis f) Kontsevich

We discuss the problem of finding the minimal dilatation among pseudo-Anosov mapping classes on a fixed closed surface. In particular, for every nonorientable closed surface of even genus, we consider

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.

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

Effective convergence of ergodic averages and cusp excursions of geodesics on moduli spaces We survey some applications of effective convergence of ergodic averages to the analysis of cusp ex

Recent results on windtree models with polygonal obstacles have linked their diffusion rate with Lyapunov exponents in stata of quadratic differentials.  The proves of these theorems follow from the

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

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

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

Mathematicians have long understood periodic trajectories on the square billiard table. In the present work, we describe periodic trajectories on the regular pentagon – their geometry, symbolic

The first part of the course will be devoted to some of the classical results about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston

The first part of the course will be devoted to some of the classical results about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston

In the principal stratum in genus two, McMullen observed that something odd happens - there is only one nonarithmetic Teichmuller curve - the one generated by the decagon.  This strange phenomenon

We study the question whether affine invariant submanifolds arising from Teichmueller dynamics are affine varieties in the sense of algebraic geometry.

Multicurves have played a fundamental role in the study of mapping class groups of surfaces since the work of Dehn. A beautiful method of describing such systems on the n-punctured disk is given by

Tiling billiards is a dynamical system in which a billiard ball moves through the tiles of some fixed tiling in a way that its trajectory is a broken line, with breaks admitted only at the boundaries

I will show how we can produce exotic representations of surface groups from the Witten-Reshetikhin-Turaev TQFT. These representations have infinite images and give points on character varieties that

Finding lattices in PU(n,1) has been one of the major challenges of the last decades.  One way of constructing a lattice is to give a fundamental domain for its action on the complex hyperbolic space.

H. Masur showed in the early 80s that almost every Teichmuller ray converges to a unique point in PMF. It is also known since a while that there are rays that have more than one accumulation point in

I will discuss joint work with Hugo Parlier concerning the shortest noncontractible loops—’systoles’—in a translation surface. In particular, we provide estimates (some sharp) on the number of

The monodromy group of a translation surface M is the Lie group spanned by all symplectic matrices arising from the homological action of closed loops at M (inside its embodying orbit closure). In the

We show that the number of closed geodesics in the flat metric on a translation surface of length at most R is asymptotic to e hR / (hR). This is joint work with Kasra Rafi

In  the  first two lectures I will try to tell (or, rather, to  give  an  idea)  of  how  Maryam Mirzakhani has counted simple  closed  geodesics on hyperbolic surfaces. I plan to briefly  mention her

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

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

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

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

a) basic definitions and examples b) strata and genus c) reduced and primitive origamis, SL(2,R) action, Veech groups d) automorphisms and affine homeomorphisms e) homology of origamis f) Kontsevich

a) basic definitions and examples b) strata and genus c) reduced and primitive origamis, SL(2,R) action, Veech groups d) automorphisms and affine homeomorphisms e) homology of origamis f) Kontsevich

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

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

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

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

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

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

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

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

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

The first part of the course will be devoted to some of the classical results about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston