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.
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 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.
The videos of the inauguration of the Grothedieck Institute, which took place on the 3rd of December in Mondovì, are now available from YouTube.
The event was held in Italian, with transations from French of Johanna Grothendieck and Laurent Lafforgue’ talks. Stil, automatic translated subtitles are available in all languages, through the relevant YouTube option.
Thanks again to all the speakers, and to the Municipality of Mondovì for the collaboration in the organization of this event!
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):
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”):
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.
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:
Tomorrow I shall leave for a short mission in Rome.
I will be a Jury member for the Ph.D. thesis “Dynamical topoi” by Jacopo Garofali (supervised by Michael McQuillan) at Tor Vergata University, for which I have also acted as a referee. The thesis contains interesting applications of toposes to dynamical systems. The defense will take place in the afternoon of the 28th.
I will also visit Sergio Barbarossa’s research group at “La Sapienza” University, giving a talk at their Department on the 27th.
I have been invited to give a talk on this occasion. The title of my presentation is Relative toposes as a generalization of locales. The abstract is as follows:
The aim of this talk is to present a way for representing relative toposes which naturally generalizes the construction of the topos of sheaves on a locale, and which is particularly effective for describing the morphisms between relative toposes in a concrete way. Our theoretical framework is based on the language of stacks and fibred sites, and provides, amongst other things, a unified setting for investigating the relationships between Grothendieck toposes as built from sites and elementary toposes as built from triposes.