EVENT DETAILS AND ABSTRACT

Title: Differential graded Banach algebras and Lie infinity-groupoids (joint work with Kai Behrend)
Speaker: Ezra Getzler
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:

We develop a generalization of Kuranishi's construction of the analytic germ of deformations of a holomorphic vector bundle where the vector bundle is replaced by a complex of vector bundles. We introduce a natural infinity-category whose objects are the Maurer-Cartan elements of a differential graded Banach algebra. We show that the quasi-isomorphisms in this category form a Lie infinity-groupoid: this is a topological version of a result of Joyal. One of the main goals of the talk is to explain what a Lie infinity-groupoid is (generalizing the definition given by Henriques).