Abstract

Goodwillie’s calculus of homotopy functors provides a means of constructing a Taylor-series-like tower of functors for a suitably nice functor of topological spaces.  Use of this “Taylor tower” has led to significant results in homotopy theory and K-theory.  Inspired by Goodwillie’s construction, Kristine Bauer, Randy McCarthy and I developed an analogous functor calculus, the discrete calculus, based on the polynomial functors of Eilenberg and Mac Lane.  In this talk, I will provide a brief introduction to these functor calculi. I will then discuss ongoing work to develop a process for creating new functor calculi and cocalculi that generalizes the methods used for the discrete calculus, and, in particular, some of the things we’ve discovered along the way.  This is joint work with Kristine Bauer, Robyn Brooks, Kathryn Hess, Julie Rasmusen, and Bridget Schreiner.