3:00–4:00 pm
Eckhart Hall, Room 202 5734 S. University Ave. Chicago, IL 60637
Height Gaps, an Arithmetic Margulis Lemma and Almost Laws
Abstract:
We discuss some open problems and some new results about the topology of arithmetic locally symmetric spaces. Among the new results is a proof of a conjecture of Gelander stating that the topology of these manifolds can be bounded just in terms of the volume. Some of the proofs are based on a resolution of a non-abelian version of Lehmer's conjecture due to Breuillard, for which we also provide a new proof coming from the study of some curious word maps called almost laws.
All notions will be explained. Based on joint projects with M. Fraczyk, J. Raimbault, Lvzhou (Joe Chen) and Homin Lee.
