Teichmuller dynamics and Hodge theory
Aix-Marseille Université - Site St Charles
3, place Victor Hugo - case 39
13331 MARSEILLE Cedex 03
The group SL(2,R) acts naturally on the set of flat surfaces of higher genus, generalizing the action on the space of flat tori. This action is naturally related to a number of classical dynamical systems, like interval exchanges and billiard flows. For example, asymptotics on a fixed surface are related to the Lyapunov exponents of the Kontsevich-Zorich (KZ) cocycle.
In this talk, I will discuss some results about the rigidity of the SL(2,R) dynamics and the KZ cocycle. By work of Eskin, Mirzakhani, and Mohammadi, orbit closures have a good local structure, in particular are manifolds. I will explain how to obtain further global restrictions, in particular proving that they are algebraic varieties.
The talk will start from the basics, assuming no background in either Teichmuller dynamics or Hodge theory.
- Simion FILIP