EVENT DETAILS AND ABSTRACT

Title: Derived Loops and Drinfeld Centers
Speaker: John Francis
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

Classically, vector bundles on the conjugation quotient G//G have a universal property with respect to Rep(G): they form its Drinfeld center. Recent joint work with David Ben-Zvi and David Nadler generalizes this result, extending work of Hinich to derived algebraic geometry. We describe a homotopy-theoretic analogue of the Drinfeld center of a monoidal stable infinity category as a Hochschild cohomology category. For the category of sheaves on X, we prove that its center is equivalent to sheaves on the derived loops LX. The structure of this category of sheaves defines an extended 2-dimensional topological quantum field theory.