Speaker: Ewain Gwynne

Title: Random conformal geometry in dimension $d\geq 3$

Abstract: There has been enormous progress in the last few decades concerning random geometric objects in two dimensions which interact nicely with conformal maps. Such objects include Schramm-Loewner evolution (SLE), Liouville quantum gravity (LQG), and discrete analogs thereof. However, much less is known about analogs of these objects in dimension $d\geq 3$. I will give an overview of a few known results and many open problems concerning random geometry in dimension $d\geq 3$. Some of the known results come from recent joint works with Jian Ding and Zijie Zhuang, with Ahmed Bou-Rabee, and with Federico Bertacoo. I will not assume any background knowledge about random geometry for $d=2$.