EVENT DETAILS AND ABSTRACT

Title: Measure rigidity and actions of lattices on manifolds
Speaker: Aaron Brown
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

I will discuss some current work in progress on actions of lattices in higher-rank Lie groups on manifolds. In particular, I’ll consider actions of lattices in SL(n,\R), n\ge 3 on (n-1)-dimensional manifolds. Conjecturally, the only such manifolds admitting actions with infinite orbits are the (n-1) dimensional projective space or sphere. I’ll outline our approach to showing this for cocompact lattices. I’ll also consider the critical dimensions appearing in Zimmer’s conjecture for actions lattices in Sl(n,C).

The new ideas are to apply arguments coming from non-uniform measure rigidity arguments for actions of higher-rank abelian groups. I’ll outline these ideas and our approach. This is joint work with Federico Rodriguez Her and Zhiren Wang based on previous joint work with David Fisher and Sebastian Hurtado.