Roughly speaking, Goodwillie calculus gives ways in which an unstable object (a space or a space-valued functor) is built up from `stable data plus extension problems'. This description takes the form of a tower of approximations, which we think of as a `Taylor series' for the space.I'll give a gentle introduction to Goodwillie calculus, explaining how to get Hilton-Milnor-type decompositions of the Goodwillie tower for certain polyhedral products, and what such decompositions are good for. This question was appealing partly because these decompositions are in a certain sense `formal' for the wedge and the product, but in different ways. All of this is joint work with Niall Taggart.

Online Talk