Talk information

Date: Sunday, May 14, 2023
Time: 10:10–11:00
Place: Schreiber 309
Speaker: Doron Puder (TAU)
Title: Spectral gaps of Cayley graphs and Schreier graphs of the symmetric group

Abstract:

Aldous’ spectral gap conjecture, proved in 2009 by Caputo, Liggett and Richthammer, states the following a priori very surprising fact: the spectral gap of a random walk on a finite graph is equal to the spectral gap of the interchange process on the same graph. This is equivalent to that for every set of transposition $A$ in the symmetric group $S_n$, the spectral gap of the Cayley graph $Cay(S_n, A)$ is identical to that of the Schreier graph depicting the action of $S_n$ on $\{1,..,n\}$ w.r.t. $A$. Can this remarkable result be generalized to other generating sets? I will discuss possible generalizations and explain what we know about them.

This is based on joint works with Ori Parzanchevski and with Gil Alon and Gadi Kozma.