Tag Archives: Topos

Talk at Deducteam – ENS Paris-Saclay

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On Friday the 3rd of May, at 10am, I will give a talk on “Deductive systems and Grothendieck topologies” at the seminar of the research group Deducteam of the École normale supérieure Paris-Saclay.

In the talk I will show that the classical proof system of geometric logic over a given geometric theory is equivalent to new proof systems based on the notion of Grothendieck topology. Remarkably, these new systems, which are related to the classsical one through topos-theoretic ‘bridges’, are computationally much better-behaved for many purposes, as I will illustrate by discussing a few notable applications.

We are looking forward to a computer implementation of these techniques allowing to exploit all the computational advantages deriving from the multiplication of points of view which is made possible by topos theory.

You can attend the talk in presence (in Room 1Z71 of the ENS Paris-Saclay) or online, at this Zoom link.

More information is available at the seminar page.

Looking forward to seeing many of you there!

Toposes and their place in mathematics: an interview for the ICCM

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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!

Interview ICCM NoticesDownload

Course on toposes at the University of Paris-Saclay

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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!

Visit to Lyon

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On Tuesday the 5th of March I will give a talk at the ENS de Lyon, in the framework of their Seminar “Logique, Mathématiques, Informatique, Raisonnement“, about the work on relative topos theory that I have been pursuing in the last years, starting with the paper Relative topos theory via stacks (with R. Zanfa), and which I am currently developing with my Ph.D. students at the Grothendieck Institute.

The seminar will take place at 18 in the Amphi A / Grande Nef 1-2 of the Campus Monod of the ENS de Lyon; you may download the poster here.

Looking forward to it!

Syntactic learning

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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.

Syntactic Learning Via Topos TheoryDownload

Slides: “Toposic Fraïssé-Galois theory and motivic toposes”

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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.

TalkICBSDownload

Videos of the Paris event of the Grothendieck Institute

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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!

Visit to China

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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.

Visions in mathematics: from Grothendieck to the present day

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The Grothendieck Institute is hosting a conference for the general public on 14 June 2023 at the Institut Henri Poincaré in Paris. This meeting, entitled “Visions in mathematics: from Grothendieck to the present day“, will explore, with talks by Mateo Carmona, Alain Connes, Stéphane Dugowson, Johanna Grothendieck, Laurent Lafforgue and myself, the issues raised by the person and visionary work of A. Grothendieck from a philosophical, literary and sociological perspective. It will also discuss mathematical themes such as topos theory and its future in today’s mathematical landscape, industrial research and the dissemination of scientific knowledge.

The conference is free of charge and open to all upon prior registration on the Institute’s website.

Looking forward to seeing many of you there!

Talk at Logica Universalis Webinar

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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!