Affine Grassmanians, Loop Groups, and Moduli of Finite Flat Group Schemes
The affine grassmanian is a certain moduli functor of vector bundles which shows up in a variety of contexts. It is not representable as a scheme, but rather as an ind-scheme. I will discuss the representability, its relationship to loop groups, and how it arises naturally in the study of moduli of vector bundles on a curve. In the second half, I will discuss how the affine grassmanian shows in my line of work in studying a certain moduli of finite flat group schemes.