U. Haifa Topology & Geometry seminar: Sunday, November 30, 2025, 17:00. Speaker: Nima Rasekh (Greifswald). Title: “Hochschild Homology of Bicategories”.
Hochschild homology was originally introduced as an invariant of associative algebras that generalizes the commutator. In subsequent decades, it has been extended both in categorical directions, such as to dg-categories, and in topological ones, such as to ring spectra. These generalizations have also enabled many fruitful interactions with other theories, such as algebraic K-theory or fixed point methods. The existence of Hochschild homology in such diverse contexts motivated Ponto to introduce a notion that can encompass the various perspectives: a shadow of bicategories. In this talk, I will show that shadows themselves admit a characterization in terms of a bicategorical version of Hochschild homology. I will then discuss various powerful applications of this perspective, such as ∞-categorical versions of shadows, Morita invariance properties, and Hochschild homology of enriched bimodules. Joint work with Kathryn Hess.
Recording:
