Appears in collection : Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

An equivariant infinite loop space machine is a functor that constructs genuine equivariant spectra out of simpler categorical or space level data. In the late 80’s Lewis–May–Steinberger and Shimakawa developed generalizations of the operadic approach and the G-space approach respectively. In this talk I will report on joint work with Bert Guillou, Peter May and Mona Merling on adapting these machines to work multiplicatively and on understanding their categorical input.