Spectral gap for random hyperbolic surfaces

par Joe Thomas

mercredi 3 déc. 2025, 14:00 → 15:00 Europe/Paris

Salle Olga Ladyjenskaïa (IHP - Bâtiment Borel)

The first non-zero eigenvalue, or spectral gap, of the Laplacian on a closed hyperbolic surface encodes important geometric and dynamical information about a surface. In this talk, I will discuss the typical size of the spectral gap for a random surface with large genus sampled with respect to the Weil-Petersson probability measure. In particular, I will explain joint work with Will Hide and Davide Macera where we obtain a spectral gap with a polynomial error rate. Our result uses a fusion of the polynomial method used in recent breakthroughs on the strong convergence of group representations with the trace formula for hyperbolic surfaces.