I will talk about recent work which studies Wilson loop expectations in lattice Yang-Mills models. In particular, I will give a representation of these expectations as sums over embedded maps. Time permitting, I will also discuss alternate derivations, interpretations, and generalizations of several recent theorems about Brownian motion limits (Dahlqvist), lattice string trajectories (Chatterjee and Jafarov) and surface sums (Magee and Puder).

This is joint work with Minjae Park and Scott Sheffield.