Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Various types of spectra and spectral measures on Schreier and Cayley graphs

Talk by Prof. Dr. Tatiana Smirnova-Nagnibeda

**Date:** 17.05.21 **Time:** 15.00 - 16.15 **Room:** ETH HG F 3

We will be interested in the Laplacian on graphs associated with finitely generated groups: Cayley graphs and more generally Schreier graphs corresponding to some natural group actions. The spectrum of such an operator is a compact subset of the closed interval [-1,1], but not much more can be said about it in general. We will discuss various techniques that allow to construct examples with different types of spectra: connected, union of two intervals, totally disconnected…, and how this depends on the choice of the generating set in the group. Types of spectral measures that can arise in these examples will also be discussed.