Séminaires : Séminaire Géométrie et dynamique dans les espaces de modules

Séminaire mensuel à l'Institut Henri Poincaré, plupart du temps mercredi de 14h à 15h salle Olga Ladyjenskaïa (ex-salle 01). Pour plus de détails voire la page web :

http://carlos.matheus.perso.math.cnrs.fr/seminaire/index.html

Monthly seminar at the Institute Henri Poincaré. It usually takes place on Wednesday from 2pm to 3pm at the room Olga Ladyjenskaïa (ex-room 01). For more details see

http://carlos.matheus.perso.math.cnrs.fr/seminaire/index.html

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.