Conformal Field Theory and Path Integrals

This lecture by Antti Kupiainen from the University of Helsinki explores the rigorous mathematical construction of Conformal Field Theory (CFT) and path integrals. Discover how CFT describes universality classes of statistical mechanics systems at critical temperatures and the small-scale behavior of quantum field theories. Learn about two canonical two-dimensional CFTs—the Liouville CFT and the Wess-Zumino-Witten CFT—and how they can be rigorously constructed using probability theory. The talk explains how their bootstrap solutions can be approached and proved through probabilistic construction, while also demonstrating a surprising correspondence between these theories that defines a "quantum" deformation of the analytic Langlands correspondence. Delivered as part of the BIMSA Colloquium series, this presentation features Kupiainen, a distinguished mathematician who has received numerous accolades including the Dannie Heineman Prize for Mathematical Physics and the Henri Poincaré Prize from the International Association of Mathematical Physics.