Abstract: 

Conformal Field Theories (CFT) are believed to describe the universal behaviour of physical systems at a second order phase transition point. They also play a central role in Quantum Field Theories of fundamental physics by describing their properties in the limits of small and large length scales. In two dimensions they are believed to have a rich mathematical structure uncovered by the  physicists Belavin, Polyakov and Zamolodchicov in 1983 with deep impacts in representation theory and geometry. However their rigorous mathematical foundations have remained a matter of debate. The lectures aim to explain a probabilistic approach to CFT based on their path integral formulation and how this can be connected to Graeme Segal’s geometric approach to conformal bootstrap, an axiomatic approach to CFT. We show how such a probabilistic formulation can be used to construct a complete bootstrap solution of a major CFT, the Liouville CFT that plays a central role in Liouville Quantum Gravity and the theory of random surfaces. Time permitting we will also explain how similar methods can be applied to Wess-Zumino-Witten models, a major class of CFTs.

Bio-Sketch

Antti Kupiainen received his PhD at Princeton and has served as a professor at Rutgers and at Helsinki. He  is a mathematical physicist who has pioneered the rigorous theory of the renormalisation group, field theory approach to turbulence as well as  the mathematical theory of stochastic quantisation and most recently probabilistic approach to Conformal Field Theories and the conformal bootstrap. For this work he has received numerous prizes among them the Henri Poincare Prize, Dannie Heineman Prize and the Georg Polya Prize.

Time

3.17, 1:30-2:30pm | 3.18, 10am-noon | 3.20, 10am-noon