## Huawei and topos theory

Apart from the initiatives I mentioned last time, Huawei set up a long term collaboration with the IHES, the Huawei Young Talents Program.

“Every year, the Huawei Young Talents Program will fund on average 7 postdoctoral fellowships that will be awarded by the Institute’s Scientific Council, only on the basis of scientific excellence. The fellows will collaborate with the Institute’s permanent professors and work on topics of their interest.”

Over the next ten years, Huawei will invest 5 million euros in this program, and an additional 1 million euros goes into the creation of the ‘Huawei Chair in Algebraic Geometry’. It comes as no particular surprise that the first chairholder is Laurent Lafforgue.

At the launch of this Young Talents Program in November 2020, Lafforgue gave a talk on The creative power of categories: History and some new perspectives.

The latter part of the talk (starting at 47:50) clarifies somewhat Huawei’s interest in topos theory, and what Lafforgue (and others) hope to get out of their collaboration with the telecom company.

Clearly, Huawei is interested in deep neural networks, and if you can convince them your expertise is useful in that area, perhaps they’ll trow some money at you.

Jean-Claude Belfiore, another mathematician turned Huaweian, is convinced topos theory is the correct tool to study DNNs. Here’s his Huawei-clip from which it is clear he was originally hired to improve Huawei’s polar code.

At the 2018 IHES-Topos conference he gave the talk Toposes for Wireless Networks: An idea whose time has come, and recently he arXived the paper Topos and Stacks of Deep Neural Networks, written jointly with Daniel Bennequin. Probably, I’ll come back to this paper another time, for now, the nForum has this page on it.

Towards the end of his talk, Lafforgue suggests the idea of creating an institute devoted to toposes and their applications, endorsed by IHES and supported by Huawei. Surely he knows that the Topos Institute already exists.

And, if you wonder why Huawei trows money at IHES rather than your university, I leave you with Lafforgue’s parting words:

“IHES professors are able to think and evaluate for themselves, whereas most mathematicians just follow ‘group thinking'”

Ouch!

## Huawei and French mathematics

Huawei, the Chinese telecom giant, appears to support (and divide) the French mathematical community.

I was surprised to see that Laurent Lafforgue’s affiliation recently changed from ‘IHES’ to ‘Huawei’, for example here as one of the organisers of the Lake Como conference on ‘Unifying themes in geometry’.

Judging from this short Huawei-clip (in French) he thoroughly enjoys his new position.

Huawei claims that ‘Three more winners of the highest mathematics award have now joined Huawei’:

Maxim Kontsevich, (IHES) Fields medal 1998

Pierre-Louis Lions (College de France) Fields medal 1994

Alessio Figalli (ETH) Fields medal 2018

These news-stories seem to have been G-translated from the Chinese, resulting in misspellings and perhaps other inaccuracies. Maxim’s research field is described as ‘kink theory’ (LoL).

Apart from luring away Fields medallist, Huawei set up last year the brand new Huawei Lagrange Research Center in the posh 7th arrondissement de Paris. (This ‘Lagrange Center’ is different from the Lagrange Institute in Paris devoted to astronomy and physics.)

It aims to host about 30 researchers in mathematics and computer science, giving them the opportunity to live in the ‘unique eco-system of Paris, having the largest group of mathematicians in the world, as well as the best universities’.

Last May, Michel Broué authored an open letter to the French mathematical community Dans un hotel particulier du 7eme arrondissement de Paris (in French). A G-translation of the final part of this open letter:

“In the context of a very insufficient research and development effort in France, and bleak prospects for our young researchers, it is tempting to welcome the creation of the Lagrange center. We welcome the rise of Chinese mathematics to the highest level, and we are obviously in favour of scientific cooperation with our Chinese colleagues.

But in view of the role played by Huawei in the repression in Xinjiang and potentially everywhere in China, we call on mathematicians and computer scientists already engaged to withdraw from this project. We ask all researchers not to participate in the activities of this center, as we ourselves are committed to doing.”

Among the mathematicians signing the letter are Pierre Cartier and Pierre Schapira.

To be continued.

## Bourbaki and Grothendieck-Serre

This time of year I’m usually in France, or at least I was before Covid. This might explain for my recent obsession with French math YouTube interviews.

Today’s first one is about Bourbaki’s golden years, the period between WW2 and 1975. Alain Connes is trying to get some anecdotes from Jean-Pierre Serre, Pierre Cartier, and Jacques Dixmier.

If you don’t have the time to sit through the whole thing, perhaps you might have a look at the discussion on whether or not to include categories in Bourbaki (starting at 51.40 into the clip).

Here are some other time-slots (typed on a qwerty keyboard, mes excuses) with some links.

• 8.59 : Canular stupide (mort de Bourbaki)
• 15.45 : recrutement de Koszul
• 17.45 : recrutement de Grothendieck
• 26.15 : influence de Serre
• 28.05 : importance des ultra filtres
• 35.35 : Meyer
• 37.20 : faisceaux
• 51.00 : Grothendieck
• 51.40 : des categories, Gabriel-Demazure
• 57.50 : lemme de Serre, theoreme de Weil
• 1.03.20 : Chevalley vs. Godement
• 1.05.26 : retraite Dieudonne
• 1.07.05 : retraite
• 1.10.00 : Weil vs. Serre-Borel
• 1.13.50 : hierarchie Bourbaki
• 1.20.22 : categories
• 1.21.30 : Bourbaki, une secte?
• 1.22.15 : Grothendieck C.N.R.S. 1984

The second one is an interview conducted by Alain Connes with Jean-Pierre Serre on the Grothendieck-Serre correspondence.

Again, if you don’t have the energy to sit through it all, perhaps I can tempt you with Serre’s reaction to Connes bringing up the subject of toposes (starting at 14.36 into the clip).

• 2.10 : 2e these de Grothendieck: des faisceaux
• 3.50 : Grothendieck -> Bourbaki
• 6.46 : Tohoku
• 8.00 : categorie des diagrammes
• 9.10 : schemas et Krull
• 10.50 : motifs
• 11.50 : cohomologie etale
• 14.05 : Weil
• 14.36 : topos
• 16.30 : Langlands
• 19.40 : Grothendieck, cours d’ecologie
• 24.20 : Dwork
• 25.45 : Riemann-Roch
• 29.30 : influence de Serre
• 30.50 : fin de correspondence
• 32.05 : pourquoi?
• 33.10 : SGA 5
• 34.50 : methode G. vs. theorie des nombres
• 37.00 : paranoia
• 37.15 : Grothendieck = centrale nucleaire
• 38.30 : Clef des songes
• 42.35 : 30.000 pages, probleme du mal
• 44.25 : Ribenboim
• 45.20 : Grothendieck a Paris, publication R et S
• 48.00 : 50 ans IHES, lettre a Bourguignon
• 50.46 : Laurant Laforgue
• 51.35 : Lasserre
• 53.10 : l’humour

## Grothendieck’s gribouillis (4)

Fortunately, there are a few certainties left in life:

In spring, you might expect the next instalment of Connes’ and Consani’s quest for Gabriel’s topos. Here’s the latest: $\overline{\mathbf{Spec}(\mathbb{Z})}$ and the Gromov norm.

Every half year or so, Mochizuki’s circle-of-friends tries to create some buzz announcing the next IUTeich-workshop. I’ll spare you the link, if you are still interested, follow math_jin or IUTT_bot_math_jin on Twitter.

And then, there’s the never-ending story of Grothendieck’s griboullis, kept alive by the French journalist and author Philippe Douroux.

Alexandre Grothendieck : une mathématique en cathédrale gothique, an article (in French) by Philippe Douroux in Le Monde, May 6th (behind paywall).

L’histoire étonnante des archives du mathématicien Alexandre Grothendieck, an article (in French) on France Inter by Mathieu Vidar, based on info from Philippe Douroux.

Les archives mystérieuses de Alexandre Grothendieck, a podcast of a broadcast on France Inter on June 10th. Interesting interview (in French) with Philippe Douroux and the French mathematician Etienne Ghys (with a guest appearance by Luc Illusie).

El enigmático legado de un genio de las matemáticas, an article (in Spanish) in El Pais, May 13th, with 8 photos of some of the Gribouillis. The two pictures in this post are taken from this article.

So, what’s the latest on the 70.000+ pages left by Grothendieck?

As far as i know, the Mormoiron part of the gribouillis is still at the University of Montpellier, and has been made available online at the Grothendieck archives.

The Lasserre part of the gribouillis is still in a cellar in Paris’ Saint-Germain-des-Prés, belonging to Jean-Bernard Gillot. The French national library cannot take possession of the notes before a financial agreement is reached with Grothendieck’s children (French law does not allow children to be disinherited).

And there’s a dispute about the price to be paid. The notes were estimated at 45.000 Euros, but some prefer to believe that they may be worth several millions of dollars.

It all depends on their mathematical content.

Unfortunately, pictures claimed to be of the Lasserre notes (such as the one above) are in fact from the Mormoiron/Montpellier notes, which do indeed contain interesting mathematics.

But, it is very unlikely that the Lasserre notes contain (math) surprises. Probably, most of them look like this one

endless lists of people deported by the Nazis to extermination camps in WW2.

Or, as Philippe Douroux is quoted in the El Pais piece: “I think it’s a treasure, maybe not a mathematical one, but a human one. It’s a descent into the hell of one the best organised brains in the world.”

The film made by Catherine Aira and Yves Le Pestipon “Alexandre Grothendieck: On the Paths of a Genius” (on the quest for G’s last hideout in the French Pyrenees) can now be watched on YouTube (with English subtitles)

## Grothendieck, at the theatre

A few days ago, the theatre production “Rêves et Motifs” (Dreams and Motives) was put on stage in Argenteuil by la Compagnie Les Rémouleurs.

The stage director Anne Bitran only discovered Grothendieck’s life by reading the front pages of French newspapers, the day after Grothendieck passed away, in November 2014.

« Rêves et Motifs » is a piece inspired by Récoltes et Semailles.

Anne Bitran: ” In Récoltes et semailles we meet a scientist who has his feet on the ground and shares our curiosity about the world around us, with a strong political engagement. This is what I wanted to share with this piece.”

Some of Grothendieck’s dessins d’enfant make their appearance. Is that one Monsieur Mathieu in the center? And part of the Hexenkuche top left? (no, see Vimeo below)

And, does this looks like the sculpture ‘Grothendieck as Shepherd’ by Nina Douglas?