## Noncommutative Geometry Seminar

**Date:** November 13, 2019

**Time:** 2:00PM - 3:00PM

**Location:** BLOC 628

**Speaker:** Tatiana Nagnibeda, University of Geneva

**Title:** *Various types of spectra and spectral measures on Schreier and Cayley graphs*

**Abstract:** 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 disconnectedâ€¦, 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.