The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds. For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. In particular --- on manifolds whose dimension is below the dimension of all algebraic examples --- Zimmer's conjecture asserts that every action is finite. With D. Fisher, S. Hurtado, we recently solved Zimmer's conjecture for actions of cocompact lattices in Sl(n,R), n>=3.

I will give an overview of our proof and explain some of the ingredients used in that proof: Zimmer cocycle superrigidity, Ratner's measure classification theorem, strong property (T), and smooth ergodic theory
of actions of higher-rank abelian groups. Speaker(s): Aaron Brown (Univ of Chicago)