## Some results that hold on every flat surface

### Time

Apr 9 2013 – 1:50pm – 2:50 pm

### Location

CH240

### Speaker

Jon Chaika (University of Chicago)

### Abstract

Recently Eskin-Mirzakhani-Mohammadi have proven a number of

powerful results about the SL_2(R) orbits of abelian differentials and

the SL_2(R) ergodic measures on the stratum. We discuss some results

motivated and enabled by this work. One result is that for

every abelian differential there is a measure on the stratum, such

that after rotating in almost every direction, the geodesic flow

equidistributes for this measure on the stratum. Another result is

that for any surface the conclusion of Oseledets multiplicative

ergodic theorem applies for the Kontsevich-Zorich cocycle. This has an

application, being explored by others, to the windtree model. This is

joint work with Alex Eskin.