From Quantum Field Theory to Geometric Representation Theory

Quantum Field Theory is a framework of fundamental physics, which in particular has played important roles in the modern development of various subjects in mathematics, including enumerative geometry, knot theory, and low-dimensional topology. On the other hand, Geometric Representation Theory is a subject in mathematics that studies a linear model of various types of symmetries using powerful techniques of algebraic geometry. In recent years, there has been much progress relating the two subjects, enriching the subject of Geometric Representation Theory. In this colloquium style talk, we will review some recent advancements on the topic. No prior knowledge of either Quantum Field Theory or Geometric Representation Theory will be assumed.