
The hype cycle of an idea
These three ideas (re)surfaced over the last two decades, claiming to have potential applications to major open problems: (2000) $\mathbb{F}_1$geometry tries to view $\mathbf{Spec}(\mathbb{Z})$ as a curve over the field with one element, and mimic Weil’s proof of RH for curves over finite fields to prove the Riemann hypothesis. (2012) IUTT, for Inter Universal Teichmuller […]

Chevalley’s circle of friends
Last week, Danielle Couty ArXiVed her paper Friendly views on Claude Chevalley (in French). From the abstract: “We propose to follow the itinerary of Claude Chevalley during the last twenty years of his life, through the words of Jacques Roubaud, Denis Guedj and Alexander Grothendieck. Our perspective is that of their testimonies filled with friendship.”…

Grothendieck stuff
January 13th, Gallimard published Grothendieck’s text Recoltes et Semailles in a fancy box containing two books. Here’s a Gtranslation of Gallimard’s blurb: “Considered the mathematical genius of the second half of the 20th century, Alexandre Grothendieck is the author of Récoltes et semailles, a kind of “monster” of more than a thousand pages, according to…

Poly
Following up on the deep learning and toposespost, I was planning to do something on the logic of neural networks. Prepping for this I saw David Spivak’s paper Learner’s Languages doing exactly that, but in the more general setting of ‘learners’ (see also the deep learning post). And then … I fell under the spell…

Grothendieck talks
In 201718, the seminar Lectures grothendieckiennes took place at the ENS in Paris. Among the speakers were Alain Connes, Pierre Cartier, Laurent Lafforgue 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…

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…

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 Huaweiclip (in French) he…

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…

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…

Princeton’s own Bourbaki
In the first half of 1937, Andre Weil visited Princeton and introduced some of the postdocs present (notably Ralph Boas, John Tukey, and Frank Smithies) to Poldavian lore and Bourbaki’s early work. In 1935, Bourbaki succeeded (via father Cartan) to get his paper “Sur un théorème de Carathéodory et la mesure dans les espaces topologiques”…