Spectral Geometry of Liouville Quantum Gravity 1
Speaker: Nathanael Berestycki
Date: Tue, Jun 24, 2025
Location: PIMS, University of British Columbia
Conference: 2025 PIMS-CRM Summer School in Probability
Subject: Mathematics, Probability
Class: Scientific
Date: Tue, Jun 24, 2025
Location: PIMS, University of British Columbia
Conference: 2025 PIMS-CRM Summer School in Probability
Subject: Mathematics, Probability
Class: Scientific
Abstract:
I will discuss Liouville Brownian motion, the canonical diffusion in the random geometry defined by Liouville quantum gravity (LQG). In particular I will present some recent results on the spectral geometry of LQG, showing that the eigenvalues satisfy a Weyl law. We will also discuss a number of striking conjectures which aim to relate LQG to a phenomenon known as "quantum chaos", which will also be explained.
