Strong convergence of typical permutation representations of surface groups

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• Ramon van Handel (Princeton University)
• Thursday 09 October 2025, 14:00-15:00
• Seminar Room 1, Newton Institute.

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OGGW03 - Spectral gaps

Suppose we draw NxN permutation matrices A,B,C,D uniformly at random fromthe set of all such matrices that satisfy [A,B][C,D]=1. What can we sayabout the spectral gap of noncommutative polynomials of these matrices,asymptotically as N goes to infinity? I will aim to explain the origin ofof such questions of strong convergence, their implications for the studyof spectral gaps of surfaces, and how a recent new development, thepolynomial method, now makes it possible to prove such results. This talkis based on joint work with Michael Magee and Doron Puder.

This talk is part of the Isaac Newton Institute Seminar Series series.

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