Algebra/Topology seminar

Ivo Dell'Ambrogio, A categorification of the representation theory of finite groups

Abstract: In joint work with Paul Balmer, we develop a theory of "Mackey 2-functors" in order capture certain phenomena that occur throughout equivariant mathematics, in domains such as equivariant stable homotopy theory, equivariant KK-theory, as well as in the ordinary linear representation theory of finite groups. By virtue of arising at the 2-categorical level, these phenomena are invisible to classical algebraic frameworks such as Dress's theory of Mackey functors. In this talk I will: provide many examples of Mackey 2-functors; motivate our axiomatisation; explain its close kinship with the ordinary theory of Mackey functors and with the theory of derivators; and describe the first applications of our theory.