|DATE||November 24 (Wed), 2021|
|TITLE||Liouville quantum gravity surfaces|
|ABSTRACT||Liouville quantum gravity (LQG) is a random fractal surface constructed from Gaussian free field (GFF), first appeared in the physics literature. LQG surface has a great importance since it describes the universal large-scale behavior of discrete random geometries. Unlike smooth two-dimensional Riemannian manifolds, LQG surfaces are too rough and possess fractal properties. In this series of talks, I will give an overview of the LQG surface and talk about its probabilistic and geometric properties.
GFF is a log-correlated Gaussian field, which is a central model of random height functions. I will briefly mention some key properties of GFF and talk about extreme value theory.