A new approach to realizing transfer systems as equivariant operads

Speaker: Ben Szczesny – Ohio State University

Abstract: Blumberg and Hill have introduced the notion of $\mathbb{N}_ \infty$-operads as an equivariant extension of $\mathbb{E}_\infty$ that can also encode norm maps – a type of twisted multiplication. It has been shown that the homotopy category of $\mathbb{N}_\infty$-operads is equivalent to a category of combinatorial objects called transfer systems. In this talk we will introduce a new construction that allows us to build operads realizing transfer systems that is both simpler than the currently available methods and, in some respects, more general as it also allows us to construct homotopy incoherent operads reminiscent of $\mathbb{E}_k$-operads. If there is time, we will also give some open problems related to our construction.