Mathematics & Computer Science

Seminars and Colloquia

Thursday, February 11, 2016

04:15 pm - 05:15 pm

Math CS Colloquium, Alex Lubotzky (Hebrew University of Jerusalem and Yale University):"Ramanujan complexes and topological expanders"

Abstract: Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 4 decades and more recently also in pure math. In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1. This question was answered recently (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by T. Kaufman and S. Evra for general d) by showing that the d-skelton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders.

Exley 121

Thursday, March 03, 2016

04:15 pm - 05:15 pm

Math CS Colloquium, Andrei S. Rapinchuk (University of Virginia):"Hearing the shape of a locally symmetric space, and arithmetic groups"

Abstract: I will discuss the famous question of Mark Kac Can one hear the shape of a drum? in the context of (compact) locally symmetric spaces. In a joint work with G. Prasad, we were able to resolve this question in many situations using our analysis of weakly commensurable arithmetic subgroups of algebraic groups. The notion of weak commensurability makes sense for arbitrary Zariski-dense subgroups and time permitting I will report on the ongoing project (joint with V. Chernousov and I. Rapinchuk) to develop a new form rigidity (called the eigenvalue rigidity) based on this concept. This work involves problems in the theory of algebraic groups of independent interest.

Exley 121