The bottom of the spectrum of a random hyperbolic surface
Mathematical Physics Seminar
4th December 2020, 2:00 pm – 3:00 pm
Online seminar, Zoom, meeting ID TBA
In this talk, I will report on work in progress with Laura Monk, where we study the bottom of the spectrum of the laplacian, on a compact hyperbolic surface chosen at random, in the limit of growing genus. We pick combinatorial ideas from the study of random regular graphs, to propose a strategy to prove that, with high probability, there are no eigenvalues below $1/4-\epsilon$.