|DATE||December 03 (Fri), 2021|
|TITLE||Random metric properties of Liouville quantum gravity|
|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.
Although the measure on the LQG surface has been well-understood, it is extremely delicate to study its metric properties. Very recently, a canonical metric associated with the LQG surface was successfully constructed. I will briefly talk about the construction of this random metric and its geometric properties, such as behaviors of geodesics.