Spectral Gaps of Random Covers of Hyperbolic Surfaces

Explore a lecture on spectral gaps of random covers of hyperbolic surfaces delivered by Frédéric Naud as part of the Hausdorff Trimester Program "Dynamics: Topology and Numbers" conference. Delve into the concept of random hyperbolic surfaces with infinite area and understand the relevant notion of spectral gap for Laplacian resonances. Discover the main result, a probabilistic version of Selberg's 3/16 theorem, developed in collaboration with Michael Magee. Learn how the proof incorporates transfer operators and zeta functions. Gain insights into this advanced mathematical topic over the course of 64 minutes, presented at the Hausdorff Center for Mathematics.