The invariant measure of the 2D Yang-Mills Langevin dynamic
Vienna Probability Seminar
Date:
Monday, December 18, 2023 15:45 - 17:00
Speaker:
Ilya Chevyrev (University of Edinburgh)
Location:
Mondi 2 (I01.01.008), Central Building
Series:
Mathematics and CS Seminar
Host:
M. Beiglböck, N. Berestycki, L. Erdös, J. Maas, F. Toninelli, E. Schertzer
Contact:
Birgit Oosthuizen-Noczil
In this talk I will discuss the problem of stochastic quantisation of Parisi-Wu in the context of Yang-Mills (YM) theories. I will explain how, after a suitable renormalisation, one can make sense of the YM Langevin dynamic on the 2D torus in a way that respects the underlying gauge symmetries and makes the 2D YM measure invariant for the dynamic. I will describe several steps in the proof of this result as well as some its consequences, including a decomposition of the YM measure into a Gaussian free field and a regular remainder. Based on joint work with Hao Shen.