Research
Research
Preprint, Utrecht University, 2026.
We identify the Goodwillie approximations of the circle as infinite loop spaces, using work of Behrens and Kuhn on the Whitehead conjecture. This reduces the computation of their homotopy groups to a stable problem, accessible through the Adams spectral sequence and computer calculations. We also develop a Goodwillie-calculus analogue of the Gray sequence relating successive stages of the tower.
Preprint, Utrecht University, 2026.
We develop foundations for metastable homotopy theory using Heuts' 2-truncated Tate coalgebras.
Master’s thesis, University of Turin, 2021.
We study natural transformations between functors built from reduced symmetric powers of pointed spaces. Using Goodwillie calculus, we develop a framework for computing their homotopy groups and carry out explicit rational and integral calculations, motivated by a connection with Ext groups between functors from free groups to abelian groups.
Some of these calculations subsequently appeared in Gregory Arone’s paper Polynomial functors from free groups to a stable infinity-category (see examples 12.11).