4:00 pm Wednesday, December 14, 2016
Groups & Dynamics: Lattice actions on manifolds and Zimmer’s conjecture by Aaron Brown (University of Chicago) in RLM 10.176
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. Recently, D. Fisher, S. Hurtado, and I 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 our proof: Zimmer cocycle superrigidity, Ratner’s measure classification theorem, strong Property (T), and smooth ergodic theory of actions of higher-rank abelian groups. Submitted by
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