UVic Dynamics and Probability Seminar: Sky Cao

In this talk, I will describe some progress towards the construction of the 3D Yang-Mills (YM) measure. In particular, I will introduce a state space of “distributional gauge orbits” which may possibly support the 3D YM measure. Then, I will describe a result which says that assuming that 3D YM theories exhibit short distance behavior similar to the 3D Gaussian free field (which is the expected behavior), then the 3D YM measure may be constructed as a probability measure on the state space. The underlying technical details involve analyzing the YM heat flow (which is a certain PDE) with random distributional initial data. This is based on joint work with Sourav Chatterjee.