Alex Furman : On some theorems of Margulis, Stuck-Zimmer, Peterson and IRS

Posted by Alexander Furman , part of the Graduate Groups and Dynamics Seminar.

At

March 20, 2019, 4 p.m.

In

612 SEO

Abstract

Margulis's Normal Subgroup Theorem states that for an irreducible lattice $\Gamma$ in a higher rank center-free semi-simple Lie group $G$ does not have normal subgroups of infinite index. Stuck and Zimmer have proved that every non-transitive p.m.p. ergodic action of $G$ is essentially free. This strengthens Margulis' NST. More recently, Peterson proved character super-rigidity for higher rank lattices, strengthening the result of Stuck-Zimmer. In the talk, I will discuss the relations between these statements and will sketch some ideas of the proofs.