Title: Derivatives and Taylor Series in Homotopy Theory
Speaker: Duncan Clark (Ohio State University)
Abstract: Functor calculus was developed by Tom Goodwillie to understand complicated functors, like K-theory, by studying simpler, polynomial-like approximations. For example, a (reduced) linear functor is one which satisfies excision. One of his main results is that a homotopy functor on pointed topological spaces admits a Taylor tower: a tower of polynomial approximations which behave eerily like the Taylor series from ordinary calculus, and which under suitable conditions converge to the original functor. In this talk, we define the major players in functor calculus and give some insight into what the derivates of a functor tell us. This talk should be accessible to all graduate students, though some basic familiarity with algebraic topology and category theory wouldn’t hurt.