Category Archives: News

Course on “Relative toposes for artificial general intelligence”

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In the forthcoming weeks, in the framework of my D’Alembert Chair at the Université Paris-Saclay, I shall give a course at the MICS Laboratory of CentraleSupélec on “Relative toposes for artificial general intelligence“.

ABSTRACT:

Topos theory can be described as the science of invariants. The theory of relative toposes consists in methods and techniques for studying toposes in relation to each other. Viewing toposes as spaces embodying information, this theory notably paves the way for the development of new, very dynamical and structural forms of modelling, both of ‘real’ entities and phenomena, and of (natural or artificial) learning processes. In particular, it naturally leads to the design of systems implementing principles of meta-learning (in the sense of learning taking place at different levels of abstraction constructed on top of each other).

The first part of the course will provide a conceptual introduction to the theory of relative toposes and its relevance for AI, while the second will present some first applications of this theory in connection with the modelling and solution of Raven progressive matrices and, more generally, of ARC-type problems.

N.C. No previous knowledge of topos theory is necessary for understanding the key ideas and methods presented in the course.

DATES:

– Thursday 26 June 2025, 14-16, Amphi SC.046 (Peugeot), Bouygues building (9 Rue Joliot Curie, 91190 Gif-sur-Yvette).
– Thursday 3 July 2025, 14-16, Amphi SC.046 (Peugeot), Bouygues building (9 Rue Joliot Curie, 91190 Gif-sur-Yvette).

Looking forward to seeing many of you there!

Toposes in Mondovì

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We are glad to announce that the fourth edition of the international school and conference on topos theory, following the previous editions “Topos à l’IHES” (2015), “Toposes in Como” (2018) and “Toposes online” (2021), will take place in Mondovì (Italy) from 3 to 11 September 2024:


For further information and registration, please visit the event website.

We look forward to seeing many of you in Mondovì!

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

On women and mathematics

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On the occasion of the release in France of the movie Marguerite’s theorem, I was interviewed at Radio France with Mélanie Guenais and Ariane Mézard about women and mathematics.

The discussion, lasting for about one hour, has touched several different themes, from statistics related to the numbers of female students and researchers in mathematics to ways to improve mathematics education at large.

You may listen to the podcast here.

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:

https://youtube.com/watch?v=videoseries%3Flist%3DPLq6qUEvr5AcooJS9PwKKisWW4x042LVxz

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!

Towards a semantic 6G

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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):

Semantics as a ‘bridge’

The links to attend the event are available from the conference webpage.

Looking forward to it!

Grothendieck Institute

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On 3 December 2022, the inaugural event of the recently founded Grothendieck Institute will take place at 3:00 p.m. in the Aula Magna of the Mondovì campus of the Polytechnic of Turin. The event, which is sponsored by the Municipality of Mondovì, will be held in Italian and will see the participation of numerous guests, including Johanna Grothendieck (Alexander’s daughter and member of the Institute’s Board of Directors), Laurent Lafforgue (member of the Institute’s Scientific Council), Gino Zaccaria (Professor of Philosophy at Bocconi University) and Nicoletta Sabadini (Professor of Computer Science at the University of Insubria). The round table and the subsequent exchange with the public will be moderated by national TV journalist Francesca Ronchin. 

The title of the event is “All’ascolto della voce delle cose. Un progetto visionario per la matematica e non solo“. The expression “all’ascolto della voce delle cose” belongs to Grothendieck himself, who said “Ce qui fait la qualité de l’inventivité et de l’imagination du chercheur, c’est la qualité de son attention, à l’écoute de la voix des choses” (“The quality of a researcher’s inventiveness and imagination is the quality of his attention, to hearing the voices of things”):

PosterPresentationGrothendieckInstituteDownload

Among the topics that will be addressed in the round table, in a way which is accessible to the general public, are basic research and its applications, scientific creativity, the figure of Alexander Grothendieck as an example of the kind of relationship that can exist between scientific studies, humanistic sensitivity and social commitment, abstraction and its relationship with art, ethics in scientific research.

Looking forward to seeing many of you there!

Conference in honor of Jean-Jacques Szczeciniarz

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Tomorrow and Friday, the 24th and 25th November 2022, a conference in honor of Jean-Jacques Szczeciniarz will take place in Paris.

In order to celebrate Jean-Jacques’ work on Copernicus and his reflections on categorial and Grothendieckian mathematics, I shall give (tomorrow at 16.00 French time) a talk entitled “De Copernic à Grothendieck: la puissance du point de vue fecond“, where I shall elaborate on the importance of fruitful points of view in Science by taking as prominent examples the Copernican revolution and Grothendieck’s unifying concept of topos.

For those who wish to attend the conference online, here are the Zoom credentials:

https://u-paris.zoom.us/j/84654497182?pwd=eVBwakRzcmNBNnNkUTJqdHNjeWhaUT09

ID: 846 5449 7182
Code: 005352

Trip to Sweden

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Tomorrow I will leave for Sweden for scientific visits to Götheborg and Stockholm.

I will be in Götheborg for participating in the

Workshop in Honour of Thierry Coquand’s 60th Birthday

My talk, entitled “Relative toposes as a generalization of locales“, will be on Thursday 25th at 10:15.

Then I shall leave for Stockholm, where I will give a colloquium lecture for the Stockholm Mathematics Centre (KTH and Stockholm University) on Wednesday 31st at 15:15.

Thanks again to the organisers of these events for their invitations, and looking forward to this trip!

Grothendieck conference

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From tomorrow, Tuesday the 24th of May, until Saturday the 28th of May, there will be, physically at Chapman University and virtually on Zoom, a conference celebrating Grothendieck’s work.

The programme, which is available from the conference website, is very rich and consists of several contributions highlighting the relevance of Grothendieck’s ideas across many different fields of knowledge.

I will give my own talk, entitled “On the ‘unifying notion’ of topos“, on Friday 27th at 10 am PST (7pm CEST).

The Zoom link to the conference is  
https://chapman.zoom.us/j/96839483231?from=addon
Meeting ID: 968 3948 3231

Looking forward to seeing many of you attending the conference!