# Mathematics Colloquium

#### Conformal Field Theory and Path Integrals

**Speaker:**
Antti Kupiainen, University of Helsinki

**Location:**
Warren Weaver Hall 1302

**Date:**
Monday, November 4, 2024, 3:45 p.m.

**Synopsis:**

Conformal Field Theory (CFT) describes universality classes of statistical mechanics systems at the critical temperature of a second order phase transition and also small scale behaviour of general quantum field theories. In physics there are two approaches to CFT, the path integral approach and the conformal bootstrap approach. I will describe two canonical two dimensional CFTs, the Liouville CFT and the Wess-Zumino-Witten CFT and explain how they can be given a rigorous construction using probability theory and how their bootstrap solution can be approached with the probabilistic construction. Furthermore the probabilistic construction allows to derive a surprising map between these two theories originally conjectured by Ribault, Teschner, Hikida and Schomerus and argued to define a “quantum” deformation of the analytic Langlands correspondence.