|DATE||November 30 (Tue), 2021|
|TITLE||Gaussian multiplicative chaos|
|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.
LQG is a random surface whose metric tensor is expressed as an exponential of GFF. It naturally arises in the scaling limit of thick points of GFF. I will briefly talk about this connection and review Kahane's theory of Gaussian multiplicative chaos.