The videos of the recent conference organized by the Grothendieck Institute at the Institut Henri Poincaré are now available from the Institute’s YouTube channel:
The event consisted in a round table with Alain Connes, Johanna Grothendieck and Laurent Lafforgue, moderated by Stéphane Dugowson and preceded by two brief presentations by Mateo Carmona, Coordinator of the Centre for Grothendieckian Studies, and myself.
We will present an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts : this unifies and generalizes Grothendieck’s theory of “Galois categories” and Fraïssé’s construction of homogeneous structures in model theory. This theory notably allows one to construct fundamental groups in many classical contexts such as finite groups, finite graphs, motives and many more. We will in particular present an approach based on it for building “motivic toposes” and investigating the independence from l of l-adic cohomology.