Time:14:00-15:30, Sunday, July 9, 2023
Venue:A1 Lecture Hall
Host:Gang Tian
Speaker:Laurent Lafforgue
Title：Glimpses on Grothendieck toposes in the perspective of AI
Biography：Laurent Lafforgue is the famous French researcher who fundamentally contributed to modern mathematics. He is the world leader in the Langlands program in positive characteristic. His proof of the Langlands correspondence for general linear groups over global fields of positive characteristic was a milestone in number theory. He was awarded the 2002 Fields Medal for his breakthrough. His recent work on functoriality conjecture in the Langlands program is another pivotal contribution. Laurent Lafforgue has made outstanding contributions, some of them jointly with Olivia Caramello, to topos theory, its applications, and interdisciplinary developments related to toposes, neural networks and AI. For twenty years he was a permanent member of IHES, the top European mathematical research institute. Since September 2001 he works at Huawei Paris.
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.
