GLIMPSES ON GROTHENDIECK TOPOSES IN THE PERSPECTIVE OF AI

*Abstract*:

Grothendieck's notion of topos is one of the broadest and richest in mathematics. It can be approached from several completely different points of view, thus making it possible to connect parts of mathematics that seemed a priori alien to each other.

Surprisingly, it is both highly abstract and "primitive" in the sense that it directly embodies basic intuitions and capacities of the human mind that would have seemed a priori pre-mathematical or meta-mathematical.

These aspects of toposes have led engineers to seize upon this notion in order to model and theorise different aspects of artificial intelligence. Some research directions are already being actively explored, while others are waiting for more mathematicians, computer scientists and engineers to be trained in the study of Grothendieck toposes.

*Essential bio*:

Student at the École Normale Supérieure de Paris, Laurent Lafforgue received his Ph.D. in 1994 at the Université d'Orsay, under the direction of Gérard Laumon. Currently research director of CNRS and researcher at Huawei Technologies, from 2000 to 2021 he was permanent professor at IHÉS.

Laurent Lafforgue has made outstanding contributions to Langlands' program in the fields of number theory and algebraic geometry .

Major distinctions for his work are:
1996 Prix et cours Peccot du Collège de France
1998 Médaille de bronze du CNRS
2000 Clay Research Award
2001 Grand prix Jacques Herbrand de l'Académie des Sciences
2002 Field Medal (during the ICM, Beijing)
2003 Chevalier de la Légion d'Honneur