C. T. McMullen - Billiards, quadrilaterals and moduli spaces

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

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

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

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

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.

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

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

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

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