Category Archives: Events

Towards a semantic 6G

Posted on by
Reply

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

Posted on by
Reply

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

Posted on by
Reply

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

Visit to Rome

Posted on by
Reply

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.

SYCO 9 in Como

Posted on by
Reply

Next week, on the 8th and 9th of September, the Ninth Symposium on Compositional Structures (SYCO 9) is taking place in Como.

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.

Looking forward to seeing many of you in Como!

Trip to Sweden

Posted on by
Reply

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!

Domoschool 2022

Posted on by
Reply

Next week I will be in Domodossola giving a research course on topos theory for the 2022 edition of the International Alpine School of Mathematics and Physics.

The title of my course is Grothendieck toposes, invariants and ‘bridges’. The course will be an introduction to the theory of Grothendieck toposes, with a specific emphasis on the invariants that one can define on them. The point of view that we shall take is the one provided by the theory of toposes as ‘bridges’, which we shall present and illustrate through a selection of notable examples. We shall also discuss the application of these techniques to the investigation and discovery of dualities, equivalences and correspondences in mathematics and beyond.

Grothendieck conference

Posted on by
1

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!

Working group on proofs and Grothendieck topologies

Posted on by
2

A working group of about 20 researchers has formed to investigate computational aspects of the methodology ‘toposes as bridges’, with particular reference to the proof-theoretic equivalences established in Chapters 3 and 8 of my book Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic ‘bridges’ and described in these slides.

Bridge between Grothendieck topologies and quotients

The organizer is Laurent Lafforgue, and the meetings will take place at the Huawei Lagrange Center for Mathematics and Computation in Paris, starting from the first one, which has happened today.

A final goal is to implement these techniques on a computer, to automatically generate mathematical results by exploiting the capacity of ‘bridges’ to significantly transform the level of complexity of notions and results. Back in 2010, when I first evoked this possibility in the paper The unification of Mathematics via Topos Theory, that idea was regarded with a lot of skepticism, as something almost too good to be true. Now, the time is ripe to start making that dream into reality.