Understanding Goodwillie towers I

Abstract

In the course of three seminars we will discuss the classic constructions of Goodwillie calculus of functors. We are interested in the applications of this theory in unstable homotopy theory and our end goal is to understand, whenever Goodwillie tower of the loop-suspension functor admits a homotopy decomposition in sense of Selick-Wu. Along the way we will try to reformulate Goodwillie calculus in simplicial language, discuss simplicial functors as models for spectras (the work by Lydakis) and try to relate Goodwillie tower to the lower central series tower for simplicial groups.

Speaker Intro

I'm working in simplicial homotopy theory and its applications in path homology and homological algebra related to groups and Lie algebras. I'm also interested in applications of deep learning in contemporary mathematics.