Groups and Dynamics Seminar

Date: October 10, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Slava Grigorchuk

Title: On the question: "Can one hear the shape of a group?" and Hulancki type theorem for graphs

Abstract: In my talk I will address the famous question of M.Kac (traced back to L.Bers and A.Weyl) "Can one hear the shape of a drum?" in the context of groups viewed as geometric objects. I will show that the answer in NO in a strong sense: there is a continuum family of 4-generated pairwise not quasi-isometric groups with the same spectrum of discrete Laplacian. Moreover each of these groups has uncountable family of amenable covering groups with the same spectrum. The arguments will be based on the construction by the speaker of groups of intermediate growth (between polynomial and exponential), and the results in the spectral theory of graphs which somehow is related to the famous Hulanicki criterion of amenability of groups in terms of weak containment of unitary representations. The talk is based on joint results with A.Dudko.