Spectral asymptotics of LQG and KPZ
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. In ongoing work with Jakob Klein we further show that second order asymptotics of the heat trace are governed by the KPZ formula. Time permitting we will discuss a conjectured connection to “quantum chaos”.