Colloquium: Monday, June 4, 2 pm. Speaker: Gregory Arone (Stockholm). Title: “Polynomial functors in topology and algebra”.

Polynomial functors were introduced in an algebraic setting by Eilenberg and Mac Lane around 1954 (but implicitly were present already in the work of Schur circa 1900). Since the advent of the calculus of functors (Tom Goodwillie in the 1990-ies), polynomial functors became applicable in topology, and beyond that in the general setting of “abstract homotopy theory”. They have been applied with considerable success to problems in algebraic K-theory, homotopy theory and geometric topology. They remain an object of active research, both for their own sake and as a tool for solving problems.

In this talk I will introduce the notion of a polynomial functor and will illustrate its usefulness via some examples from topology and algebra.