The Interplay between Random Geometry and CFT

Abstract

Conformal field theory has its origins in the early 1970s via an operator algebra formalism used to study the Ising model, and the seminal 1984 paper of Belavin, Polyakov, and Zamolodchikov cemented the role of CFT as a uniquely special type of QFT. This talk will describe aspects of the interplay between CFT and random geometry. Introduced by Schramm in the early 2000s, random geometry uses tools from probability theory and complex analysis to study scaling limits of two-dimensional statistical mechanics models. This approach allowed mathematicians to rigorously verify many calculations made by physicists using CFT. More recently, ideas from CFT have allowed mathematicians to bring novel insight into their understanding of the underlying random geometry.