Doug Pickrell: Introduction to random conformal geometry

This is an expository talk. There are at least five different reasonable ways of introducing randomness for a (conformal) surface. It is a highly nontrivial fact (due to Sheffield and Miller, and others) that these notions are all essentially equivalent. I will begin by briefly recalling the most naive approach, which leads to the Brownian map (attributable to LeGall and Miermont; google John Baez, The Brownian Map, for a brief introduction). The rest of the talk is about `Liouville quantum gravity' (inspired by Polyakov), which is related to `Gaussian multiplicative chaos' (see Sheffield's 'What is a Random Surface?', arXiv:2203.02470 for a brilliant introduction to the other approaches and relations). I will try to explain some of the relevant ideas from conformal field theory in a relatively elementary way. On September 10th and 11th Morris Ang will discuss some applications of random geometry.