Kathryn Hess: THH, shadows, and bicategorical traces

Abstract: Joint work with Nima Rasekh. The theory of shadows is an axiomatic, bicategorical framework that generalizes topological Hochschild homology (THH) and satisfies analogous important properties, such as Morita invariance. I’ll explain how to use Berman's extension of THH to bicategories to prove that there is an equivalence between functors out of THH of a bicategory and shadows on that bicategory. As an application we provide a new, conceptual proof that shadows are Morita invariant and construct the shadow of THH of enriched infinity-categorical bimodules. In the first hour of the talk, I’ll provide an introduction to shadows and explain why they’re interesting, before discussing my work with Nima.