Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Bram Petri
Affiliation:

Jussieu
Date:

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.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/11255