Extremal Hyperbolic Surfaces and the Selberg Trace Formula

par Prof. Bram Petri (IMJ-PRG)

lundi 11 avr. 2022, 16:00 → 17:15 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

The Selberg trace formula provides a link between the length spectrum and the Laplacian spectrum of a hyperbolic surface. 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 hyperbolic surface of a given genus with the largest kissing number or the largest spectral gap? 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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IHES Covid-19 regulations:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

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