Speaker: Zhonghui Sun,  MSU

Title: Twisted bicategorical shadows and traces

Abstract:
Bicategorical shadows, defined by Ponto, provide a framework which generalizes (topological) Hochschild
homology.  Bicategorical shadows have important properties, such as Morita invariance, and allow one to generalize the symmetric monoidal trace to a bicategorical trace. Topological Hochschild homology (THH), which is an essential component to the trace methods approach for algebraic K-theory, is a key example of a bicategorical shadow.

In recent years, equivariant versions of topological Hochschild homology have emerged. In particular, for a C_n-ring spectrum there is a theory of C_n-twisted THH, constructed via equivariant norms. However, twisted THH fails to be a bicategorical shadow. In this talk, we will explain a new framework of equivariant bicategorical shadows and explain why twisted THH is a g-twisted shadow. We also explore g-twisted bicategorical traces.