**Speaker**: Sebastian M. CioabÄƒ, University of Delaware

**Date**: Thu, Sep 17, 2015

**Time**: 14:00 - 15:00

**Venue**: Large Meeting Room

**Title**: Eigenvalues of graphs, small expanders and non-backtracking random walks

**Abstract**:

The eigenvalues of a graph provide important structural information. In particular, expansion and random walk properties of a graph are closely related to the graph spectrum. In this talk, I will discuss my recent work (with Koolen, Nozaki and Vermette) studying the largest order of a regular graph of given valency and second eigenvalue and (with my student Peng Xu) generalizing some results involving the mixing time of non-backtracking random walks of Alon, Benjamini, Lubetzky and Sodin.