On the spectral geometry of Liouville quantum gravity
Holder： Nathanaël Berestycki（University of Vienna）
Time：2025-04-07 14:00-15:00
Location：Siyuan Lecture Hall，Zhi Hua Building-225
Abstract:
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".
About the Speaker:
Nathanaël Berestycki holds the chair of Stochastics at the University of Vienna since 2018. Prior to this (and after PhD studies at Ecole Normale Supérieure in Paris and Cornell University, as well as a postdoctoral fellowship at the University of British Columbia in Vancouver) he was a Professor of Probability at the University of Cambridge. He has been an associate editor of numerous journals, including the Annals of Probability, and was an invited speaker at the International Congress of Mathematical Physics (ICMP) in 2024.
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