I am glad to share the pdf of my interview by Nathan Carruth, which will appear in print in the Notices of the International Consortium of Chinese Mathematicians.
Thanks again to Nathan for his excellent questions, which allowed me to discuss about so many different aspects of toposes and their relevance for mathematics and beyond!
In the coming weeks, starting from Thursday the 14th of March, I will give an introductory course on topos theory at the Laboratoire MICS of CentraleSupélec (Université Paris-Saclay).
More details, including the content and schedule of the lectures, can be found at the course webpage.
Everybody is welcome!
The slides of my recent talk at the AI workshop at RL China are available below.
In this presentation I propose an interpretation of learning processes in terms of the notions of mathematical theory and proof, and advocate for the importance of empowering artificial learnings systems with large formal vocabularies that will serve for expressing the concepts (and relations between them) that they will learn from data.
The aim is to obtain more robust and structured forms of learning with generalisation capabilities, and greater resilience and adaptability, mimicking the distinctive features of human intelligence.
We also consider this project as an essential step for arriving at a toposic theory of semantic information; indeed, syntax and semantics are interwined (think, for instance, of the syntactic construction of classifying toposes).
I look forward to experimentally testing these ideas with our team at the Lagrange Center in Paris.
A new paper, written jointly with my Ph.D. student Léo Bartoli, is available from the ArXiv:
The paper carries out a systematic investigation of the functors between sites which induce morphisms between relative toposes.
It culminates in a generalisation of Diaconescu’s theorem for relative toposes, formulated in the language of fibrations and stacks according to the foundations for relative topos theory introduced in the paper Relative topos theory via stacks.
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.
On Wednesday the 17th of May at 4 CET I will give a talk at the Logica Universalis Webinar on the contents of my paper “The unification of Mathematics via Topos Theory”, originally written in 2010 and recently published in the book “Logic in Question” (Studies in Universal Logic, Springer-Birkhäuser, 2022).
The talk will be accompanied by a short presentation of the Grothendieck Institute by Laurent Lafforgue.
Looking forward to seeing many of you there!
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!
The slides of my talk at the Workshop on Semantic Information and Communication are available for download: