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# Goodwillie's calculus of functors

## Introductory Workshop: Algebraic Topology January 27, 2014 - January 31, 2014

January 27, 2014 (11:00 AM PST - 12:00 PM PST)
Speaker(s): Michael Ching (Amherst College)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

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Abstract

The calculus of homotopy functors provides a systematic way to approximate a given functor (say from based spaces to spectra) by so-called polynomial' functors. Each functor F that preserves weak equivalences has a Taylor tower' (analogous to the Taylor series of ordinary calculus) which in turn is built from homogeneous pieces that are classified by certain `derivatives' for F. I will review this material and consider the problem of how the Taylor tower of F can be reconstructed from its derivatives. We will discuss some important examples built from mapping spaces. Then. if time permits, I will us this approach to give a classification of analytic functors from based spaces to spectra and try to describe some connections to the Goodwillie-Weiss manifold calculus

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