Speaker: Pavel Safronov
Title: Higher Azumaya algebras and invertible TFTs
Abstract: Azumaya algebras are associative algebras which are invertible as objects of the Morita bicategory. They can be explicitly characterized as central separable algebras. In this talk I will describe an analogous characterization of invertible E_n-algebras (algebras over the operad of little n-disks) in an arbitrary infinity-category. In the case of braided tensor categories (n = 2) I will give a list of checkable conditions; in particular, nondegenerate (possibly, non-semisimple) braided tensor categories are invertible. I will also mention a relationship of this result to non-semisimple 3-dimensional TFTs. This talk is based on joint work with A. Brochier, D. Jordan and N. Snyder.