Kathryn Hess (Lausanne): Hochschild shadows for motivic spaces and spectra

This talk was part of the conference "Homotopy theory, K-theory, and trace methods" held in July 2023 at Radboud University, Nijmegen, The Netherlands in honor of Bjørn Ian Dundas' 60th birthday.

Abstract: The theory of shadows, first introduced by Ponto, is an axiomatic, bicategorical framework that generalizes (topological) Hochschild homology and satisfies analogous important properties, such as Morita invariance and agreement. I’ll describe a general model category theoretic framework in which to define Hochschild homology of “ring objects” and to show that it is a shadow and explain how it applies to motivic spaces and spectra. (based on work with K. Adamyk, T. Gerhardt, I. Klang, and H. Kong and with A. Beaudry, M. Kedziorek, M. Merling, and V. Stojanoska)