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    My favourite tags on MathOverflow are big-lists, big-picture, soft-question, reference-request and the like. Often, answers to such tagged questions contain sound reading advice, style: “road-map to important result/theory X”. Two more K to go, so let’s spend some more money. One of the problems with my master course on algebraic geometry is that the students... Continue reading

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    A couple of days ago, there was yet another article by Philippe Douroux on Grothendieck’s Lasserre writings “Inestimables mathématiques, avez-vous donc un prix?” in the French newspaper Liberation. Not that there is much news to report. I’ve posted on this before: Grothendieck’s gribouillis, Grothendieck’s gribouillis (2), and more recently Where are Grothendieck’s writings? In that... Continue reading

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  • 12/23/16--12:10: Stirring a cup of coffee
  • Please allow for a couple of end-of-semester bluesy ramblings. I just finished grading the final test of the last of five courses I lectured this semester. Most of them went, I believe, rather well. As always, it was fun to teach an introductory group theory course to second year physics students. Personally, I did enjoy... Continue reading

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    Geometers will tell you there are two ways to introduce affine schemes. You can use structure sheaves. That is, compute all prime ideals of your ring and turn them into a space. Then, put a sheaf of rings on this space by localisation. You’ll get your ring back taking global sections. Or, you might try... Continue reading

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  • 02/27/17--00:30: The subway singularity
  • The Boston subway is a complex system, spreading out from a focus at Park Street. On March 3rd, the Boylston shuttle went into service, tying together the seven principal lines, on four different levels. A day later, train 86 went missing on the Cambridge-Dorchester line. The Harvard algebraist R. Tupelo suggested the train might have... Continue reading

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  • 03/01/17--13:35: The geometry of football
  • Soon, we will be teaching computational geometry courses to football commentators. If a player is going to be substituted we’ll hear sentences like: “no surprise he’s being replaced, his Voronoi cell has been shrinking since the beginning of the second half!” David Sumpter, the author of Soccermatics: Mathematical Adventures in the Beautiful Game, wrote a... Continue reading

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  • 07/18/17--11:57: Moonshine for everyone
  • Today, Samuel Dehority, Xavier Gonzalez, Neekon Vafa and Roger Van Peski arXived their paper Moonshine for all finite groups. Originally, Moonshine was thought to be connected to the Monster group. McKay and Thompson observed that the first coefficients of the normalized elliptic modular invariant \[ J(\tau) = q^{-1} + 196884 q + 21493760 q^2 +... Continue reading

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    In several of his talks on #IUTeich, Mochizuki argues that usual scheme theory over $\mathbb{Z}$ is not suited to tackle problems such as the ABC-conjecture. The idea appears to be that ABC involves both the additive and multiplicative nature of integers, making rings into ‘2-dimensional objects’ (and clearly we use both ‘dimensions’ in the theory... Continue reading

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    Since mid May the Montpellier part of Grothendieck’s gribouillis are online and for everyone available at the Archives Grothendieck. The story is well-known. End of June 1990, Grothendieck phoned Jean Malgoire warning him to come asap if he wanted to safeguard the better part of G’s mathematical archive, for he was making a bonfire… A... Continue reading

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  • 07/26/17--08:28: Life on Gaussian primes
  • At the moment I’m re-reading Siobhan Roberts’ biography of John Horton Conway, Genius at play – the curious mind of John Horton Conway. In fact, I’m also re-reading Alexander Masters’ biography of Simon Norton, The genius in my basement – the biography of a happy man. If you’re in for a suggestion, try to read... Continue reading

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    Next week, the brand new séminaire « Lectures grothendieckiennes » will kick off on Tuesday October 24th at 18hr (h/t Isar Stubbe). There will be one talk a month, on a tuesday evening from 18hr-20hr. Among the lecturers are the ‘usual suspects’: Pierre Cartier (October 24th) will discuss the state of functional analysis before Grothendieck […]

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    Getting mathematics into Nature (the journal) is next to impossible. Ask David Mumford and John Tate about it. Last month, John Duncan, Michael Mertens and Ken Ono managed to do just that. Inevitably, they had to suffer through a photoshoot and give their university’s PR-people some soundbites. CAPTION In the simplest terms, an elliptic curve […]

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    Earlier today, John Duncan (of moonshine fame) emailed he was unable to post a comment to the previous post: “I went to post a comment but somehow couldn’t convince the website to cooperate.” There’s little point in maintaining a self-hosted blog if people cannot comment on it. If you tried, you got this scary message: […]

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  • 11/19/17--09:18: The latest on Mochizuki
  • Once in every six months there’s a flurry of online excitement about Mochizuki’s alleged proof of the abc-conjecture. It seems to be that time of the year again. The twitter-account of the ever optimistic @math_jin is probably the best source for (positive) news about IUT/ABC. He now announces the latest version of Yamashita’s ‘summary’ of […]