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Extremal hyperbolic manifolds and the Selberg trace formula

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Bram Petri
Mon, 16/05/2022 - 11:00 - 12:00

Virtual talk.

The Selberg trace formula provides a link between the length spectrum and the Laplacian spectrum of a hyperbolic manifold.  I will speak about a joint project with Maxime Fortier Bourque in which we are using this formula to probe extremal problems in hyperbolic geometry. These are questions of the form: what is the largest possible kissing number or the largest spectral gap of a hyperbolic manifold of bounded volume? Concretely, I will explain the general principle of our method, which is inspired by ideas from the world of Euclidean sphere packings. Moreover, I will explain why the Klein quartic, the most symmetric Riemann surface in genus 3, solves one of our extremal problems.

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