Vertex algebras and moduli of Higgs bundles I

Motivated by a physics construction in 4d N=2 superconformal field theories, mathematicians have studied a class of vertex algebras with a number of interesting relations with the cohomology of moduli spaces of stable Higgs bundles of a curve C. We will discuss basic definitions and constructions in the theory of vertex algebras, and discuss examples, including Arakawa's construction of class S VOAs.