F1 World Seminar

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.

Higher Structures Seminar

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!

Visit to CentraleSupélec

Tomorrow (Thursday the 9th of March) I shall visit the research laboratory in Mathematics and Computer Science of CentraleSup√©lec, where I shall give a seminar at 14.00 on toposes as ‘bridges’ and their applications to several topics in artificial intelligence.

Looking forward to fruitful scientific exchanges at the interface of mathematics, computer science and engineering!

Slides: “Toposes as ‘bridges’ for mathematics and artificial intelligence”

The slides of my talk at the Workshop on Semantic Information and Communication are available for download:

Towards a semantic 6G

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!

Colloquium talk at Warwick

On Friday the 3rd of March at 5pm CET I will give a talk on toposes as ‘bridges’ at the Mathematics Colloqium of the University of Warwick.

The talk will be streamed through Microsoft Teams: to attend it, click here.

Thanks again to the organisers Sam Chow and Tobias Grafke for their kind invitation. Looking forward to seeing many of you there!

Fibred sites and existential toposes

I have just uploaded to the ArXiv a new paper, entitled “Fibred sites and existential toposes“.

The paper introduces, the context of relative topos theory via stacks, the new notions of existential fibred site and of existential topos of such a site. These concepts allow us to develop relative topos theory in a way which naturally generalizes the construction of toposes of sheaves on locales and also provides a framework for investigating the connections between Grothendieck toposes as built from sites and elementary toposes as built from triposes.

The paper also contains a fibred generalisation of the ideal-completion of a preorder site, a construction which has played a key role in the development of formal topology since the eighties:

We expect this construction to find several applications, in particular in connection with the generation of dualities from multiple representations of toposes in terms of fibred preorder sites (in the spirit of this paper), but also in Logic; indeed, applications to the construction of completions of doctrines will be provided in a forthcoming paper by my doctoral student Joshua Wrigley.

Lastly, the paper provides an explicit description of the hyperconnected-localic factorization of a geometric morphism in terms of internal locales, with applications to the construction of alternative syntactic sites for the classifying topos of a theory.

I take this opportunity to send to all of you my Season’s Greetins and very best wishes for the New Year!

UPDATE: Slides presenting the contents of the paper are available here.

On Copernicus and Grothendieck

The slides of my recent talk at the conference in honor of Jean-Jacques Szceciniarz are available here:

The talk presents an analogy between the role of the Sun in Copernicus’ vision and that of Grothendieck toposes as ‘bridges’ between different mathematical theories, by building on the general notion of a ‘bridge’ object:

The Sun as a ‘bridge’ object

Interview for Radio3 Scienza

Today’s episode of the Italian national radio Radio3 Scienza was entirely devoted to the newly inaugurated Grothendieck Institute. I was interviewed by Roberta Fulci together with Laurent Lafforgue and Johanna Grothendieck, who both participated in the inaugural event on Saturday.

You may listen to the recording here.