​I will talk about some recent work on Yang-Mills theory and its connection to the theory of random surfaces. In particular, Wilson loop expectations (important observables in Yang-Mills) can be represented as surface sums in two settings:
​- 2D continuum Euclidean Yang-Mills for classical Lie groups of any matrix size N (based on joint work with Joshua Pfeffer, Scott Sheffield, and Pu Yu)
- Any dimensional lattice Yang-Mills for classical Lie groups of any matrix size N and any inverse temperature β (based on joint work with Sky Cao and Scott Sheffield) In addition, our probabilistic approaches provide alternative derivations and interpretations of several recent theorems, including Brownian motion limits (Dahlqvist), lattice string trajectories (Chatterjee and Jafarov), and surface sums (Magee and Puder).