Thematic Seminar: Geometry: New Techniques for Zimmer's Conjecture
Seminar | January 18 | 4:10-5 p.m. | 740 Evans Hall
David Fisher, Indiana University
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 history and motivation, I will discuss a very recent result, proving many cases of the main conjecture. In this talk I will emphasize connections to homogeneous dynamics and particularly to issues of escape of mass that arise in the case of lattices which are not cocompact.