Tue, 17 Feb 2026
16:00
16:00
L6
Graph and Chaos Theories Combined to Address Scrambling of Quantum Information (with Arkady Kurnosov and Sven Gnutzmann)
Uzi Smilansky
Abstract
Given a quantum Hamiltonian, represented as an $N \times N$ Hermitian matrix $H$, we derive an expression for the largest Lyapunov exponent of the classical trajectories in the phase space appropriate for the dynamics induced by $H$. To this end we associate to $H$ a graph with $N$ vertices and derive a quantum map on functions defined on the directed edges of the graph. Using the semiclassical approach in the reverse direction we obtain the corresponding classical evolution (Liouvillian) operator. Using ergodic theory methods (Sinai, Ruelle, Bowen, Pollicott\ldots) we obtain closed expressions for the Lyapunov exponent, as well as for its variance. Applications for random matrix models will be presented.
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