# Optimal Spectral Gaps

I'll discuss spectral gaps in the following contexts:

- d-regular graphs

- locally symmetric spaces e.g. hyperbolic manifolds

- finite dimensional unitary representations of discrete groups e.g. free groups, surface groups

Of particular interest are spectral gaps that are in some a priori sense optimal or almost optimal.

The discussion will center on recent developments giving new examples of (almost) optimal spectral gaps.

## Date

## Affiliation

The Institute for Advanced Study