On the spectral geometry of Liouville quantum gravity (Nathanael Berestycki, University of Vienna)

03.03.2025 16:15 – 18:00

In this talk we will discuss the spectral geometry of the Laplace-Beltrami operator associated to Liouville quantum gravity. In particular we will show that the eigenvalues a.s. obey a Weyl law. This result (joint work with Mo Dick Wong) comes from an analysis of the LQG heat trace, which homogenises despite overwhelming pointwise fluctuations.
I will also discuss some conjectures which suggest a connection to "quantum chaos", and report on some ongoing work with Alcalde and Klein on the heat trace expansion.

Lieu

Conseil Général 7-9, Room 1-15, Séminaire Math Physics

entrée libre