Modul: MAT772 Geometrie-Seminar

## Random walks on Ramanujan graphs and complexes

Dr. Ori Parzanchevski talk

**Date:** 27.02.19 **Time:** 15.45 - 18.00 **Room:** ETH HG G 43

Ramanujan graphs are finite graphs which behave (in some sense) like an infinite tree. They have remarkable properties, such as minimal mixing rate and diameter, which found applications both in computer science and in pure mathematics. Ramanujan complexes are finite simplicial complexes which behave like infinite affine buildings, or symmetric spaces for p-adic Lie groups. Random walks on these complexes present a remarkable behavior, which leads to new applications in probability, group theory, and computer science. Based on joint works with M. Chapman, S. Evra, K. Golubev, E. Lubetzky, A. Lubotzky and P. Sarnak.