11:00–12:45, 14:15–16:00
Nathanael Berestycki
(Vienna)
On the spectral geometry of Liouville quantum gravity.
In these talks we will discuss the spectral geometry of the Laplace-Beltrami operator associated to Liouville quantum gravity. Over the course of two lectures, our goals will be to:
- Explain how eigenvalues and eigenfunctions for LQG are defined;
- Show that the eigenvalues a.s. obey a Weyl law (joint work with Mo Dick Wong). This is closely related to the short time asymptotics of the LQG heat kernel;
- Discuss the second term in the Weyl law and its relation to the KPZ (Knizhnik-Polyakov-Zamolodchikov) scaling relation;
- Finally we will talk about some conjectures which suggest a rather beautiful connection to a phenomenon called quantum chaos.