Thursday, February 8, 2018
02/08/2018 - 4:15pm to 5:15pm
Lattices in higher rank simple Lie groups are known to be extremely rigid. Examples of this are Margulis' superrigidity theorem, which shows they have very few linear represenations, and Margulis' arithmeticity theorem, which shows they are all constructed via number theory. Motivated by these and other results, in 1983 Zimmer made a number of conjectures about actions of these groups on compact manifolds. After providing some historyand motivation, I will discuss a recent result that makes dramatic progress on the conjecture in all cases and proves it in many of them. I willplace some emphasis on surprising connections to other areas of mathematics that arise in the proof.