IAS Physics Group Meeting
A Probabilistic Approach to Liouville CFT
The Institute for Advanced Study requires that all adult visitors, collaborators, conference and on-campus seminar attendees and outside vendors coming to the Institute are required to have completed a COVID-19 vaccination and booster in order to enter the IAS campus. Individuals must be prepared to present proof of vaccination if asked and are expected to follow the Institute's Covid-19 Procedures. Masks are optional while indoors. Additional information can be found at:
https://www.ias.edu/covid-19-procedures
Abstract: Liouville theory was introduced by Polyakov in 1981 as the theory governing the conformal factor in the summation over all 2d Riemannian metrics. In recent years it has undergone extensive study in the probability community, and numerous CFT predictions have been established at a mathematical level of rigor. In this talk we will first explain how one can use probability theory to rigorously define Liouville theory in the path integral approach. In the second part we will survey the main mathematical achievements of this program, including, proof of the DOZZ formula, the conformal bootstrap, properties of conformal blocks, and integration over moduli space. We will also attempt to highlight novel intuitions and formulas coming from probability.