Conformal Field Theories: Randomness and Geometry

Overview

We propose a workshop focussing on the burgeoning area at the interface of Conformal Field Theory (abbrv. CFT), probability and geometry. In recent years, Liouville Conformal Field Theory has emerged as a fundamentally important model of two-dimensional random geometries, akin to Brownian motion being a fundamental model for random functions. The significance of such CFTs is underpinned by considerations from high energy physics, dating as far back as the groundbreaking works of Polyakov in the 1980s. In spite of their foundational importance in physics, putting these ideas on a solid mathematical foundation has proved to be a notoriously difficult challenge over the years. Recently, this area has witnessed a blossoming of mathematical progress, spurred on in part by its interactions with probability theory. In particular, recent advances leverage classical probabilistic tools such as Gaussian Multiplicative Chaos and Gaussian Free Fields, as well as breakthroughs in modern stochastic PDEs (such as regularity structures) and stochastic quantization. Some of this progress is also related to the mathematics of Yang Mills theory, wherein the existence of a mass gap is one of the famous Millennium Problems of the Clay Mathematics Institute. The aim of this workshop is to bring together leading experts working at this interface. In addition to cutting-edge research discussions, one of the goals is to introduce this active area to regional researchers working in relevant disciplines, so as to spur research activities and collaborations on this highly prospective topic. In particular, we intend to invite a number of young researchers (at the level of early stage faculty, postdocs and senior PhD students) so as to initiate them into this vibrant research area.