Grothendieck talks

In 2017-18, the seminar Lectures grothendieckiennes took place at the ENS in Paris. Among the speakers were Alain Connes, Pierre Cartier, Laurent Laforgue and Georges Maltsiniotis.

Olivia Caramello, who also contributed to the seminar, posts on her blog Around Toposes that the proceedings of this lectures series is now available from the SMF.

Olivia’s blogpost links also to the YouTube channel of the seminar. Several of these talks are well worth your time watching.

If you are at all interested in toposes and their history, and if you have 90 minutes to kill, I strongly recommend watching Colin McLarthy’s talk Grothendieck’s 1973 topos lectures:

In 1973, Grothendieck gave three lectures series at the Department of Mathematics of SUNY at Buffalo, the first on ‘Algebraic Geometry’, the second on ‘The Theory of Algebraic Groups’ and the third one on ‘Topos Theory’.

All of these Grothendieck talks were audio(!)-taped by John (Jack) Duskin, who kept and preserved them with the help of William Lawvere. They constitute more than 100 hours of rare recordings of Grothendieck.

This MathOverflow (soft) question links to this page stating:

“The copyright of all these recordings is that of the Department of Mathematics of SUNY at Buffalo to whose representatives, in particular Professors Emeritus Jack DUSKIN and Bill LAWVERE exceptional thanks are due both for the preservation and transmission of this historic archive, the only substantial archive of recordings of courses given by one of the greatest mathematicians of all time, whose work and ideas exercised arguably the most profound influence of any individual figure in shaping the mathematics of the second half od the 20th Century. The material which it is proposed to make available here, with their agreement, will form a mirror site to the principal site entitled “Grothendieck at Buffalo” (url: ).”

Sadly, the URL is still missing.

Fortunately, another answer links to the Grothendieck project Thèmes pour une Harmonie by Mateo Carmona. If you scroll down to the 1973-section, you’ll find there all of the recordings of these three Grothendieck series of talks!

To whet your appetite, here’s the first part of his talk on topos theory on April 4th, 1973:

For all subsequent recordings of his talks in the Topos Theory series on May 11th, May 18th, May 25th, May 30th, June 4th, June 6th, June 20th, June 27th, July 2nd, July 10th, July 11th and July 12th, please consult Mateo’s website (under section 1973).

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.

Lockdown reading : SNORT

In this series I’ll mention some books I found entertaining, stimulating or comforting during these Corona times. Read them at your own risk.



This must have been the third time I’ve read The genius in by basement – The biography of a happy man by Alexander masters.

I first read it when it came out in 2011.

Then, in conjunction with Genius at play – The Curious Mind of John Horton Conway Conway’s biography by Siobhan Roberts, in july 2017, which is probably the best way to read this book.

And, then again last week, as Simon Norton‘s work pops up wherever I look, as in the previous post.

It takes some time to get used to the rather chaotic style (probably used because that’s how Masters perceives Norton), and all attempts at explaining Simon’s mathematics can better be skipped.

The book tries to find an answer as to why a child prodigy and genius like Simon Norton failed to secure a safe place in academics.

Page 328:

Simon’s second explanation of his loss of mathematical direction is heartbreaking. Now that Conway has fled to America, there is no one in the mathematical world who will work with him.

They say he is too peculiar, too shabby, too old.

His interests are fixed in mathematics that has had its day. His brilliance is frigid. His talent, perfectly suited to an extraordinary moment in algebraic history (the symmetry work at Cambridge during the early 1970s and 1980s) is out of fashion.

This may give the impression that Norton stopped doing good math after Conway left for Princeton in 1985. This is far from true.

Norton’s Wikipedia page mentions only post 1995 publications, which in itself is deplorable, as it leaves out his contributions to the ATLAS and his seminal paper with Conway on Monstrous moonshine.

Here’s Alexander Masters talking about ‘Genius in my basement’

I’ll leave you with a nice quote, comparing Monstrous Moonshine to a Sainsbury’s bag on Jupiter.

Page 334:

This much I do know: Monstrous Moonshine links the Monster to distant mathematics and the structure of space in ways that are as awe-inspiring to a man like Simon as it would be to an astronaut to step out of his space machine on Jupiter, and find a Sainsbury’s bag floating past. That’s why it’s called ‘Moonshine’, because mathematicians can even now hardly believe it.

‘I think’, said Simon, standing up from his berth and shaking crumbs and clotted blobs of oil and fish off his T-shirt onto the covers, ‘I can explain to you what Moonshine is in one sentence.’

When he really tries, Simon can be a model of clarity.

‘It is,’ he said, ‘the voice of God.’

Ps, wrt. SNORT.

Escher’s stairs

Stairways feature prominently in several drawings by Maurits Cornelis (“Mauk”) Escher, for example in this lithograph print Relativity from 1953.



Relativity (M. C. Escher) – Photo Credit

From its Wikipedia page:

In the world of ‘Relativity’, there are three sources of gravity, each being orthogonal to the two others.
Each inhabitant lives in one of the gravity wells, where normal physical laws apply.
There are sixteen characters, spread between each gravity source, six in one and five each in the other two.
The apparent confusion of the lithograph print comes from the fact that the three gravity sources are depicted in the same space.
The structure has seven stairways, and each stairway can be used by people who belong to two different gravity sources.

Escher’s inspiration for “Relativity” (h/t Gerard Westendorp on Twitter) were his recollections of the staircases in his old secondary school in Arnhem, the Lorentz HBS.
The name comes from the Dutch physicist and Nobel prize winner Hendrik Antoon Lorentz who attended from 1866 to 1869, the “Hogere Burger School” in Arnhem, then at a different location (Willemsplein).



Stairways Lorentz HBS in Arnhem – Photo Credit

Between 1912 and 1918 Mauk Escher attended the Arnhem HBS, located in the Schoolstraat and build in 1904-05 by the architect Gerrit Versteeg. The school building is constructed around a monumental central stairway.



Arnhem HBS – G. Versteeg 1904-05 – Photo Credit



Plan HBS-Arnhem by G. Versteeg – Photo Credit

If you flip the picture below in the vertical direction, the two side-stairways become accessible to figures living in an opposite gravitation field.



Central staircase HBS Arnhem – Photo Credit

There’s an excellent post on the Arnhem-years of Mauk Escher by Pieter van der Kuil. Unfortunately (for most of you) in Dutch, but perhaps Google translate can do its magic here.