Equivariant Localization in Factorization Homology and Vertex Algebras from Supersymmetric Gauge Theory

I will introduce factorization algebras and their factorization homology, following Beilinson-Drinfeld and Francis-Gaitsgory, and explain how these generalize the notions of vertex algebras and their conformal blocks. I will give the definition of an equivariant factorization algebra on a variety with group action, and prove an analogue of the equivariant localization theorem for factorization homology. Finally, I will explain a new family of constructions of factorization algebras on curves and manifest relations between them (in particular yielding concrete results about vertex algebras) which are motivated by higher dimensional physics via the preceding localization principle.