Kaif Hilman: Multiplicative norms on equivariant algebraic K-theory

Abstract: An important source of examples of algebraic K-theory spectra are those coming from stable categories equipped with a symmetry by a finite group G. Being a highly structured invariant, one might expect that such K-theory spectra admit the so-called G-equivariant power operations or
"multiplicative norms". In this talk, I will present a work-in-progress attaining these extra structures when G is a 2-group via the formalism of parametrised higher category theory. This, in particular, refines the Green functor structure of Barwick-Glasman-Shah on K-theory. In other settings, such structures have been enlisted in solving various conjectures and thus could be an indispensable tool in the suite of structures available on equivariant K-theory.