MATH 465-2: Factorization Algebras

Roughly, this class will be about studying one fundamental object in two different guises. Let X be an algebraic curve over a field k, and let G be some algebraic group over X . We assume for this lecture that G splits trivially as G0 ×X , but this is not necessary for what we will do in the course. The fundamental object we will study is the collection of G-bundles on X . We will consider two approaches to understanding this example: from a topological standpoint and from an algebraic geometric one. First, let’s work topologically. For simplicity let k =C. Then the space of G-bundles on X is equivalent to the mapping space: BunG(X ) ' Map(X (C),BG0(C)).