Diagram Categories in Homotopy Theory CRG Seminar: Ben Szczesny

Equivariant operads provide a powerful framework for encoding homotopic algebraic structures hidden in the non-equivariant setting, specifically those incorporating norm and transfer maps. These structures are organized by combinatorial objects called transfer systems.

This talk presents a novel approach to constructing operads from a given transfer system. By looking at certain restrictions of the coinduction functor, our method is more direct and flexible, bypassing the need for building cofibrant resolutions, or universal spaces as done in previous constructions. This allows us to construct a wider range of equivariant operads, including ones that are related to $E_k$-operads. We will also talk about work joint with Chan, Cho, Mehrle, Ocal, Osorno, and Verdugo which extends this construction to realizing compatible pairs of transfer systems as equivariant operad pairs, which can be used to encode equivariant homotopy ring structures.