- 微局部分析和应用讨论班

Spectral distribution of twisted Laplacian on random hyperbolic surfaces of large genus

组织者

陈曦 , 金龙

演讲者

龚禹霖

时间

2021年12月17日 10:00 至 11:00

地点

1129B

摘要

Inspired by quantum ergodicity in graph theory, E. le Masson and T. Sahlsten consider quantum ergodicity on a sequence of hyperbolic surfaces which converge to the hyperbolic plane in the sense of Benjamini-Schramm. A natural question is the relation between the spectral theory and topology of hyperbolic surfaces. M. Mirzakhani's contribution to the moduli space shows that we can study the spectral theory under some geometric assumption with high probability. In this series of talk, we will review L. Monk's work on the spectral distribution of Laplacian on random hyperbolic surfaces of large genus and present our work in progress on the spectral distribution of twisted Laplacian in the same setting. This can be regarded as an analog of N. Anantharaman's work on twisted Laplacian for a fixed hyperbolic surface.