Seminar 4.9.13

Some results that hold on every flat surface


Apr 9 2013 – 1:50pm – 2:50 pm




Jon Chaika (University of Chicago)


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.