Orbits closures for the action of SL(2,R) on moduli spaces.

There is an action of SL(2,R) on the moduli space of a compact Riemann surface which is expected to
have similar rigidity properties as in the theory of unipotent flows on homogeneous spaces.
In this talk we will discuss a joint work with Eskin and Mirzakhani in which orbits closures of this action are studied.
The main ingredients are a measure rigidity theorem of Eskin and Mirzakhani,
and a certain avoidance principle which we develop using ideas of Margulis.

This talk is supported by the Mrs. Hepsa Ely Silliman Memorial Fund