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Mercoledì 8 Aprile alle ore 13.00, Davide Macera (Universität Bonn) terrà il seminario di Probabilità e Fisica Matematica dal titolo "The spectral gap of some models of random hyperbolic surfaces".
Abstract: In this talk, I will introduce two models of random (smooth) hyperbolic surfaces, namely the random cover model and the Weil-Petersson model. I will then focus on the Laplace–Beltrami operator on random compact surfaces of genus g sampled with these models and discuss two recent results stating that such operator has no eigenvalues below 1/4 − g^(-c) as g grows large. These results, and the study of the spectrum of random hyperbolic surfaces in general, are motivated by some open questions from the theory of quantum chaos that I will discuss as well. The proofs make use of the notion of strong convergence for random operators and of the polynomial method, recently introduced by Chen, Garza-Vargas, Tropp and Van Handel. In the Weil-Petersson case, this gives a simpler proof of a stronger version of a celebrated recent result by Anantharaman and Monk.
Il seminario si svolgerà in presenza presso il Dipartimento di Matematica e Fisica, L.go San Leonardo Murialdo, 1 - aula B308.
