L. Liechti - Minimal dilatations on nonorientable surfaces

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

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

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

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

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

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

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

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

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

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