Inbar Klang: Equivariant Hochschild theories from a shadow perspective

Abstract: Bicategorical shadows, de fined by Ponto, provide a useful framework that generalizes classical and topological Hochschild homology. I'll review this framework and introduce the equivariant Hochschild invariants we will discuss, twisted THH and Hochschild homology for Green functors. I will then talk about joint work with Adamyk, Gerhardt, Hess, and Kong, in which we prove that these equivariant Hochschild invariants are bicategorical shadows, from which we deduce that they satisfy Morita invariance. We also show that they receive trace maps from an equivariant version of algebraic K-theory.