Conformal welding in Liouville quantum gravity: recent results and applications

Liouville quantum gravity (LQG) is a natural model for a random fractal surface with origins in conformal field theory and string theory. A powerful tool in the study of LQG is conformal
welding, where multiple LQG surfaces are combined into a single LQG surface. The interfaces between the original LQG surfaces are typically described by variants of the random fractal curves known as Schramm-Loewner evolutions (SLE). We will present a few recent conformal welding results for LQG surfaces and applications to the integrability of SLE and LQG partition functions. Based on joint work with Ang and Sun and with Lehmkuehler.