Abstract:
I will give an introduction to noncommutative ergodic theory and discuss a new framework of (commutative) ergodicity based on SAT (strongly approximate transitive) actions. These will give rise to a noncommutative generalization of a theorem of Nevo and Zimmer about factors of certain nonsingular actions that naturally arise when studying lattices of higher rank Lie groups. I will explain the main ideas behind its proof, which are new even in the commutative case.
The talk is based on ongoing work with Uri Bader.