Speaker: Fabien Morel
Date: March 12, 2026
Affiliation: LMU Munich

Abstract: In this talk I will try to explain how $\mathbb{A}^1$-homotopy theory provides new types of invariants which can be used to distinguish rational smooth projective varieties over a field. I will give a brief recollection and basic computations in $\mathbb{A}^1$-homotopy and try to explain these invariants, two important ones of them being the $\mathbb{A}^1$-fundamental group sheaf and the cellular $\mathbb{A}^1$-chain complex, the latter having been recently found in collaboration with A. Sawant. I will give explicit examples of computations and results, mostly concerning rational smooth projective surfaces over a perfect field, which is itself already nontrivial.

This work is based on my two main collaborations in the past 15 years, with A. Asok and more recently with A. Sawant.