Tue, 27 Jan 2026
16:00
16:00
L6
Spectral gaps of random hyperbolic surfaces
William Hide
Abstract
Based on joint work with Davide Macera and Joe Thomas.
The first non-zero eigenvalue, or spectral gap, of the Laplacian on a closed hyperbolic surface encodes important geometric and dynamical information about the surface. We study the size of the spectral gap for random large genus hyperbolic surfaces sampled according to the Weil-Petersson probability measure. We show that there is a c>0 such that a random surface of genus g has spectral gap at least 1/4-O(g^-c) with high probability. Our approach adapts the polynomial method for the strong convergence of random matrices, introduced by Chen, Garza-Vargas, Tropp and van Handel, and its generalization to the strong convergence of surface groups by Magee, Puder and van Handel, to the Laplacian on Weil-Petersson random hyperbolic surfaces.
Tue, 20 Jan 2026
16:00
16:00
L6
Joint Moments of CUE Characteristic Polynomial Derivatives and Integrable Systems
Fei Wei
(University of Sussex)
Abstract
In this talk, I will begin by giving some background on the joint moments of the first-order derivative of CUE characteristic polynomials, as well as the polynomials themselves, evaluated inside or on the boundary of the unit disk. I will then introduce some of my recent work on this topic and discuss its connections to Painlevé equations. Finally, I will list a few interesting and largely unexplored problems in this area. This talk draws on collaborative work with Thomas Bothner, on some work with Nicholas Simm, and on additional collaborations with Theodoros Assiotis, Mustafa Alper Gunes, and Jon Keating.
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Decoupling generalised configuration spaces on surfaces
Basualdo Bonatto, L
Transactions of the American Mathematical Society
The week will celebrate locally led initiatives and events across departments, colleges, societies, sports teams and more. This year’s theme is “The top 5 things to do for the environment as a [...]".
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Neural networks for learning macroscopic chemotactic sensitivity from microscopic models
Erban, R
SIAM Journal on Life Sciences