Height Gaps, the Margulis Lemma and Almost Laws

Seminar: 
Colloquium
Event time: 
Thursday, December 9, 2021 - 4:15pm
Location: 
Zoom
Speaker: 
Sebastian Hurtado
Speaker affiliation: 
University of Chicago
Event description: 

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. The tools in the proofs include an arithmetic version of the classical Margulis lemma about discrete subgroups of Lie groups and  makes use of the existence of certain 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.