UVictoria Dynamics and Probability Seminar: Mo Dick Wong

The Liouville quantum gravity (LQG) surface, formally defined as a 2-dimensional Riemannian manifold with conformal factor being the exponentiation of a Gaussian free field, is closely related to random planar geometry as well as scaling limits of models from statistical mechanics. In this talk we consider the bounded, simply connected setting, and explain the Weyl's law for the asymptotics of the eigenvalues of the (random) Laplace-Beltrami operator. We also discuss a few open problems about the spectral geometry of LQG. This is a joint work with Nathanael Berestycki.