Clover May

Representations of Mackey functors and equivariant homotopy theory

An algebra’s representation type, tame or wild, determines whether it is possible to describe all its indecomposable representations in a meaningful way. Mackey functors, which are representations of the Mackey algebra, were introduced by Dress and Green to encode operations like restriction and induction in representation theory. They play a central role in equivariant homotopy theory, where homotopy groups are replaced by homotopy Mackey functors. In this talk, I will discuss the representation type and derived representation type of cohomological Mackey algebra using quivers, as well as some consequences in equivariant homotopy theory. This is joint work with Jacob Grevstad.