I am glad to share the slides of my recent talk at the ICBS Satellite Conference on Algebraic and Arithmetic Geometry, where I explained how Fraïssé theory and Galois theory can be extended and linked through a unified topos-theoretic framework that can possibly be applied to the problem of constructing motives and understanding the “independence of l” properties of l-adic cohomology.
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.
Enjoy the videos!
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).
I will also give a plenary talk on the 12th at the ICBS Satellite Conference on Algebraic and Arithmetic Geometry on Toposic Galois-Fraïssé theory and motivic toposes; the abstract is as follows:
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.
The slides of my introductory course to relative toposes recently given at the Lagrange Center are now available:
The video of my recent talk at the Higher Structures Seminar is now available:
Tomorrow, Wednesday the 22nd of March, at 14:30 CET, I shall give a talk on toposes as ‘bridges’ at the F1 World Seminar.
The talk can be attended through Zoom; to receive the link to connect, you have to subscribe to the seminar’s mailing list.
Further information is avaiable at the Seminar’s webpage.
Tomorrow, Tuesday the 13th of March, I will give an online introductory talk to the theory of toposes as ‘bridges’ at the Higher Structures Seminar of the Feza Gursey Center for Physics and Mathematics at 16:45 (Istanbul local time) or 14:45 (CET).
You can attend the talk through Zoom, by clicking on this link and inserting the following credentials: Meeting ID: 969 5659 6842; Passcode: 442777.
Looking forward to seeing many of you there!
Tomorrow (Thursday the 9th of March) I shall visit the research laboratory in Mathematics and Computer Science of CentraleSupélec, where I shall give a seminar at 14.00 on toposes as ‘bridges’ and their applications to several topics in artificial intelligence.
Looking forward to fruitful scientific exchanges at the interface of mathematics, computer science and engineering!
The slides of my talk at the Workshop on Semantic Information and Communication are available for download:
I am happy to give a talk tomorrow at the “Workshop on Semantic Information and Communication” held at the Lagrange Mathematics and Computing Research Center in Paris.
The workshop, which takes place on the 7th and 8th of March, is entitled “Towards a semantic 6G” and gathers experts from different fields whose research can contribute to the development of new conceptual architectures for communication based on semantic information.
As I shall explain in my talk, topos theory is relevant for the goals of semantic communication, and AI techniques based on semantic information more generally, in several different ways. In particular, given the capacity of toposes of embodying the semantics of a great variety of situations, using toposes as ‘bridges’ enables effective transfers of knowledge across different ways of expressing information (formalized as different ways of presenting toposes):
The links to attend the event are available from the conference webpage.
Looking forward to it!