Speaker: Zhonghui Sun (Michigan State University)

Title: Equivariant Bicategorical Shadows and Traces

Abstract:  Bicategorical shadows, defined by Ponto, provide a framework that 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), an essential component
of 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. (Contact person: Hannah Housden)