SYCO 9 in Como

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!

ACAI conference in Dubai

On Tuesday the 6th of September at 10 CET I will give (online) a talk at the ACAI conference 2022 (International Conference on Advances in Computing Technologies and AI), which takes place in Dubai from the 6th to the 8th of September.

The title of the talk is “On primality conditions and residue number systems“; an abstract follows.

I will present a research programme aimed at investigating generalized primality conditions through residue number systems. Sieve methods from analytic number theory have proved to be very effective tools in addressing problems concerning prime numbers, such as, most notably, the Goldbach’s conjecture. Still, these methods are mostly based on analytic estimations rather than on structural considerations about residue number systems. We propose to experimentally study, through suitable computer programs, complementary sets of solutions to systems of congruences, in order to eventually formulate theoretical conjectures about their behavior and obtain insights, in particular, on the difficult problem of effectively characterizing the natural order relation on numbers in terms of modular representations. This should lead to a unified framework in which different problems such as the Goldbach’s conjecture and the twin prime conjecture can be constructively investigated under a common roof as part of an abstract theory of generalized primality conditions.

The subject of residue number systems has fascinated me since my teenage years, when I started pondering about these issues and developing a unifying framework for investigating generalized primality conditions. This subject is actually strictly related to topos theory, as the central result in the theory, namely the Chinese Remainder Theorem, can be interpreted as some kind of sheaf condition.

I am convinced that this subject would greatly benefit from extensive experimentations on a computer aimed at formulating theoretical conjectures about the behavior of modular representations of numbers (much as in the spirit of the discovery of the quadratic reciprocity law). This is why I accepted to give a talk at this congress, which gathers some of the main experts in computing with residue number systems. Thanks again to the organizers for their invitation: I’m greatly looking forward to the conference!

Trip to Sweden

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

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.

Videos of the Grothendieck Conference

The videos of the conference in honour of Grothendieck held in May at Chapman University are now available from Youtube.

My own talk at the conference was entitled “The unifying ‘notion’ of topos“:

The slides can be downloaded here. A written text of my presentation will be available soon.

Talk at inter-disciplinary conference of the theme of “Construction”

Tomorrow, I will give at Timeworld Paris 2022, an interdisciplinary conference organized by Laurence Honnorat’s company Innovaxiom, a popularizing talk on my research work entitled “Comment construire des ‘ponts’ en mathématiques?”.

A full program of the event is available at the conference website.

I hope to see many of you there!

UPDATE: The slides of my talk are available here.

Grothendieck conference

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
Meeting ID: 968 3948 3231

Looking forward to seeing many of you attending the conference!

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.