Algebra/Topology seminar

Speaker: Thomas Blom

Title: A generalization of the Arone-Ching chain rule

Abstract:

The chain rule of Arone-Ching is a celebrated result in
Goodwillie calculus and can be seen as a categorification of the chain
rule from ordinary calculus. Given two functors from the category of
spaces or spectra to itself, this chain rule describes how one can
reconstruct the derivatives of the composite from the derivatives of the
individual functors.

In this talk I will describe ongoing joint work with Max Blans, where we
aim to give an alternative proof of the chain rule of Arone-Ching. This
new approach has the advantage of working in much greater generality,
where the category of spaces or spectra can be replaced by any suitable
∞-category. Moreover, we give a new construction of the derivatives that
is lax monoidal. As a corollary, one obtains that the derivatives of any
monad can be given the structure of an operad, a result that has long
been believed to be true.

If time permits, I will also discuss how one can deduce a result of
Knudsen on higher enveloping algebras from the Snaith splitting.