Colloquium Mathematical Sciences

Abstract: Lattice gauge theories are a family of spin models on lattices that appear in the quantum field theory description of the standard model of physics and are a central object of interest in the physics literature. They are related to models such as the Ising model and percolation theory but have more complicated geometrical properties where the random paths appearing in other models are often replaced with random surfaces. I will describe the background of these models (both in physics and in math), several interesting open questions that could win you a million dollars, and some exciting peculiarities of this model that make them different from other related models.