**Using Topology to Solve Strongly Coupled
Quantum Field Theories**

Zohar Komargodski

(Simons Center for Geometry and Physics)

Abstract: 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.