There is a very rich interplay between certain supersymmetric four-dimensional gauge theories, the quantum geometric Langlands program and vertex algebras. The key ingredient for all three are master chiral algebras that serve as functors between representation categories. I will present a few theorems concerning a family of vertex superalgebras called the large N=4 superconformal algebras at central charge -6 and explain how they confirm some conjectures originating from physics and geometry.

The talk takes its place at RIMS 006.