Algebraic Geometry Seminar: Ezra Getzler, Northwestern University

Abstract: Using techniques from the theory of Banach algebras, Kuranishi constructed an analytic germ of the moduli space of deformations of a holomorphic vector bundle on a compact complex manifold. In order to extend his results to deformation theory of perfect complexes, we introduce higher analytic stacks, which are simplicial Banach analytic varieties satisfying a horn filler condition modeled on that satisfied by Kan complexes. We show that there is a natural way to attach a higher analytic stack to a Banach algebra, and apply this to the deformation theory of perfect complexes. This is a joint work with Kai Behrend.