Modules over factorization spaces and factorization algebras

Factorization spaces (introduced by Beilinson and Drinfeld as "factorization monoids") are non-linear analogues of factorization algebras. They can be constructed using algebro-geometric methods, and can be linearised to produce examples of factorization algebras, whose properties can be studied using the geometry of the underlying spaces. In this talk, we will recall the definition of a factorization space, and introduce the notion of a module over a factorization space, which is a non-linear analogue of a module over a factorization algebra. As an example and an application, we will introduce a moduli space of principal $G$-bundles with parabolic structures, and discuss how it can be linearised to recover modules of the factorization algebra associated to the affine Lie algebra corresponding to a reductive algebraic group $G$.