## Beyond Spectral Gaps

**Date:**
29 September - 3 October 2019

**Location: ** Mathematical Institute, University of Oxford

**Event type:**
CRC Workshop

**Organisers: ** Emmanuel Breuillard (Cambridge) and Assaf Naor (Princeton)

The goal of this workshop is to bring to Oxford leading experts in the various areas of mathematics and theoretical computer science with an interest in the spectral analysis of graphs and its many applications within mathematics. Expander graphs have now become a ubiquitous tool in much of theoretical computer science and attention has focused in the last decade or so, on the one hand, on applications of these methods to other, seemingly unrelated questions both within pure mathematics and within combinatorics and computer science, and on the other hand, to the development of generalizations of the idea of spectral gap. Our goal is to focus on those exciting recent developments where the goal has not been simply to establish a spectral gap in any given situation, but to obtain more refined spectral information with it or from it. Topics will include interlacing polynomials, strong property (T), monotone expanders, local spectral gaps, small-set expansion, affine sieve, non-linear spectral gaps, matrix expanders, high-dimensional expanders, etc.

This workshop is one of the two events composing *Pansu’s Fest*. It will be preceded by the conference *Geometry and Analysis: Celebrating the Mathematics of Pierre Pansu*. Participants in either of the events are welcome to attend the other event as well.