Institut für Mathematik


Modul:   MAT971  Seminar über stochastische Prozesse

Can you hear the shape of Liouville quantum gravity (LQG)?

Vortrag von Prof. Dr. Nathanaël Berestycki

Sprecher eingeladen von: Prof. Dr. Jean Bertoin

Datum: 25.10.23  Zeit: 17.15 - 18.45  Raum: Y27H12

'We obtain a Weyl law for the eigenvalues of Liouville Brownian motion: the n-th eigenvalue grows linearly with n, with the proportionality constant given by the Liouville measure of the domain and a certain deterministic constant which is computed explicitly and is, surprisingly, strictly greater than its Riemannian counterpart. After explaining this result and its context, as well as some related estimates pertaining to the small-time behaviour of the heat kernel, I hope to also present a number of conjectures on the spectral geometry of LQG.

These relate both to the behaviour of eigenfunctions (suggesting intriguing connections with so-called "quantum chaos") and to that of eigenvalues, for which we conjecture a connection to random matrix statistics.

This is joint work with Mo-Dick Wong (Durham).'