# Thomas Blom: Goodwillie calculus and the functional derivative

**Time: **
Wed 2021-12-01 10.15 - 11.15

**Location: **
Kräftriket, House 6, Room 306 (also on Zoom)

**Participating: **
Thomas Blom (Stockholm University)

**Abstract:**

Goodwillie calculus can be seen as a categorification of ordinary calculus, where the real line is replaced either by the category of (pointed) spaces or by the category of spectra and where functions are replaced by functors between the respective categories. As in ordinary calculus, there is a way of defining derivatives, which can then be used to approximate the original functor in a way that is similar to how Taylor series can be used to approximate functions.

In this talk, I will discuss a generalization of Goodwillie calculus to functors between categories of diagrams. The analogy mentioned above indicates that this should be a categorification of some kind of “calculus for functionals”. It turns out that this is indeed the case and that concepts such as the functional derivative admit analogues in Goodwillie calculus.

If time permits, I will also mention some things about the relation of this work with parametrized homotopy theory.