Zohar Komargodski, Colloquium - Using Topology to Solve Strongly Coupled Quantum Field Theories

I will begin by describing an interacting model in Quantum Mechanics where exact results about the ground state can be established by using tools from topology. I will then argue that such tools are also useful for tackling interesting problems in Quantum Field Theory. In particular, I will review Yang-Mills theory and argue that using topology one can make several predictions about its possible phases.