The slides of my talk at the Workshop on Semantic Information and Communication are available for download:
Slides: “Toposes as ‘bridges’ for mathematics and artificial intelligence”
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Tag Archives: Topos
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):
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!
Video of Timeworld talk
The video of my talk at Timeworld 2022 is available from YouTube:
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:
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.
Visit to Rome
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.
Domoschool 2022
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: la moisson
The podcast of today’s broadcast at France Culture “Grothendieck: la moisson” is already available on the Radio website, which also provides several references for the general public to learn more about toposes and Grothendieck’s vision.
The associated Twitter account can be accessed here.
Thanks again to Nicolas Martin and all the staff of “La méthode Scientifique” for their invitation! I look forward to join you again in a few weeks, always with Alain Connes and Laurent Lafforgue, for the second part of the broadcast.
An update: a transcription of the emission by Denise Chemla is available here.