### 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 $1/4-\epsilon$.

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