The spectral gap of Weil-Petersson random cusped hyperbolic surfaces
Vortrag von Dr. Yuhao Xue
Datum: 22.04.26 Zeit: 17.15 - 18.45 Raum: Y27H12
The Weil-Petersson metric on the moduli space of hyperbolic surfaces with $g$ genus and $n$ cusps is of finite volume, and hence induce a probability measure and a model of random cusped surfaces. The study of nearly optimal spectral gap for random closed hyperbolic surfaces is a great breakthrough in recent years. In this talk, we consider the Weil-Petersson random cusped hyperbolic surfaces, and show a uniform lower bound of the spectral gap when $n=o(\sqrt{g})$. We will carefully introduce the knowledge of Weil-Petersson random hyperbolic surfaces and the spectrum in the beginning. The talk is based on the joint work with Yuxin He and Yunhui Wu.