Optimal Spectral Gaps

June 3, 2024
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.