Absolute Galois groups and Graph Theory

par Oussama Rayen Hamza

jeudi 22 janv. 2026, 14:00 → 15:00 Europe/Paris

M7-411 (ENS Lyon)

Graph products, along with their filtrations and cohomology rings, are central to geometric group theory and have recently found significant applications in Galois theory.

 

In this talk, I will present recent results by Maire, Minac, Tân, and myself on Pythagorean fields. In the same spirit as the work of Snopce-Zalesskii and Blumer-Quadelli-Weigel, we introduce, using Right Angled Artin groups, a new necessary condition for absolute Galois groups. The main arguments come from filtration techniques and Minac's PhD thesis. As an application, we exhibit the first example of a pro-2 group that is not the maximal pro-2 quotient of an absolute Galois group but satisfies both the Bloch-Kato and Minac-Tân conjectures on filtrations and cohomology rings.