Ilya Chevyrev: Stochastic quantization of Yang-Mills, Part 2

Speaker
Ilya Chevyrev, University of Edinburgh

Abstract
In this talk I will present recent works on the analysis of the stochastic quantisation equations of 2- and 3-dimensional gauge theories. It turns out that these equations, which are systems of singular stochastic partial differential equations, can be renormalised to admit local-in-time solutions that respect the underlying symmetries of the theory. Furthermore, in the case of “pure” Yang-Mills theories in dimension 2, one can show that the associated Yang-Mills (Gibbs) measure is invariant for the dynamic. Although this 2D Yang-Mills measure is exactly solvable, the study of the dynamic can surprisingly reveal new analytic properties of the measure. Based on joint works with Ajay Chandra, Martin Hairer, and Hao Shen.