北京雁栖湖应用数学研究院

舟木 直久 , 吴劲松

Antti Kupiainen

2025年03月26日 17:00 至 19:00

A6-101

Zoom 388 528 9728 (BIMSA)

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 and proved with the probabilistic construction. Furthermore the probabilistic construction allows to prove a surprising correspondence between these two theories originally conjectured by Ribault, Teschner, Hikida and Schomerus and argued by Teschner and Gaiotto to define a “quantum” deformation of the analytic Langlands correspondence of Etingof, Frenkel and Kazhdan.

Kupiainen completed his undergraduate education in 1976 at the Technical University of Helsinki and received his Ph.D. in 1979 from Princeton University under Thomas C. Spencer (and Barry Simon) with thesis Some rigorous results on the 1/n expansion. As a postdoc he spent the academic year 1979/80 at Harvard University and then did research at the University of Helsinki. He became a professor of mathematics in 1989 at Rutgers University and in 1991 at the University of Helsinki. In 1984/85 he was the Loeb Lecturer at Harvard. He was several times a visiting scholar at the Institute for Advanced Study. He was a visiting professor at a number of institutions, including IHES, University of California, Santa Barbara, MSRI, École normale supérieure, and Institut Henri Poincaré. He was twice an invited speaker at the International Congress of Mathematicians; his ICM talks were in 1990 at Kyoto on Renormalization group and random systems and in 2010 at Hyderabad on Origins of Diffusion. From 2012 to 2014 he was the president of the International Association of Mathematical Physics. From 1997 to 2010 he was on the editorial board of Communications in Mathematical Physics. In 2010 he received the Science Award of the city of Helsinki. He received an Advanced Grant from the European Research Council (ERC) for 2009–2014. In 2022 he received (with Gawedzki) the Dannie Heineman Prize for Mathematical Physics. In 2024, he received the Henri Poincaré Prize from the International Association of Mathematical Physics.