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.
From the 10th to the 26th of July I will be visiting the BIMSA, a world-class research institution established by the Chinese Ministry of Science and Technology and led by Prof. Shing-Tung Yau, to participate in the Inaugural International Congress of Basic Science (ICBS).
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.