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Seminar on microlocal analysis and applications
Spectral distribution of twisted Laplacian on random hyperbolic surfaces of large genus
Spectral distribution of twisted Laplacian on random hyperbolic surfaces of large genus
Organizers
Xi Chen
,
Long Jin
Speaker
Yulin Gong
Time
Friday, December 17, 2021 10:00 AM - 11:00 AM
Venue
1129B
Abstract
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.