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. [full_width_image] [/full_width_image] If you’re in for a suggestion, try… Read more »

Grothendieck’s gallery No. 154

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… Read more »

How to dismantle scheme theory?

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… Read more »

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 +… Read more »

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… Read more »

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… Read more »

Forgetting can’t be that hard, can it?

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… Read more »

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… Read more »

Where are Grothendieck’s writings? (2)

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… Read more »

how much to spend on (cat)books?

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. [section_title text=”Category theory”] [full_width_image] [/full_width_image] One of the problems with my master course on algebraic… Read more »

  • stories

    G-spots : Olmet-et-Villecun

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    Before we start the quest for the final G-spot, hopefully in time for Grothendieck’s 85th birthday, one more post on Alexandre’s ‘hippy-days’. In the second part of Allyn Jackson’s “The Life of Alexandre Grothendieck” she tells the story that AG, while touring the US to spread the gospel of the eco-mouvement “Survivre et Vivre” (the… Read more »

  • stories

    G-spots : Massy

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    One week from now, Alexandre Grothendieck will turn 85. Today, we’ll have a glance at his ‘wilder years’, the early 70ties, when he resigned from the IHES and became one of the leading figures in the French eco-movement. This iconic picture is from those days The text reads: “Schurik entre les “frères ennemis” Gaston Galan… Read more »

  • stories

    G-spots : Mormoiron

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    With Grothendieck’s 85th brithday coming up, march 28th, we continue our rather erratic quest to locate the spots that once meant a lot to him. Ever wondered what Grothendieck’s last-known hideout looked like? Well, here’s the answer: (h/t gruppe eM) And, here’s the story. One of the stranger stories to be found on the web… Read more »

  • stories

    G-spots : Vendargues

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    In a couple of days, on march 28th, Alexandre Grothendieck will turn 85. To mark the occasion we’ll run a little series, tracking down places where he used to live, hoping to entice some of these villages in the south of France to update their Wikipedia-page by adding under ‘Personnalités liées à la commune’ the… Read more »

  • stories

    16 ways to capture a lion (in 1938)

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    A classic among mathematical jokes is the paper in the August/September 1938 issue of the American Mathematical Monthly “A contribution to the mathematical theory of big game hunting” by one Hector Petard of Princeton who would marry, one year later, Nicolas Bourbaki’s daughter Betti. claimtoken-511b561b7a5a2 There are two main sources of information on the story… Read more »

  • math, stories

    The empty set according to bourbaki

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    The footnote on page E. II.6 in Bourbaki’s 1970 edition of “Theorie des ensembles” reads If this is completely obvious to you, stop reading now and start getting a life. For the rest of us, it took me quite some time before i was able to parse this formula, and when i finally did, it… Read more »

  • stories

    5 unfortunate French logicians

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    According to Jean van Heijenoort, the sad state of logic in France after WW2 was largely caused by the untimely death of several key French logicians/mathematical philosophers. Prepping for my course on the history of mathematics, starting next week, i’m trying out a couple of tools, such as Timeline JS. Below, a mini timeline of… Read more »

  • featured

    Scottish solids, final(?) comments

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    In the spring of 2009 I did spend a fortnight dog-sitting in a huge house in the countryside, belonging to my parents-in-law, who both passed away the year before. That particular day it was raining and thundering heavily. To distract myself from the sombre and spooky atmosphere in the house I began to surf the… Read more »

  • stories

    From the Noether boys to Bourbaki

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    Next year I’ll be teaching a master course on the “History of Mathematics” for the first time, so I’m brainstorming a bit on how to approach such a course and I would really appreciate your input. Rather than giving a chronological historic account of some period, I’d like this course to be practice oriented and… Read more »

  • math, number theory

    Farey symbols in SAGE 5.0

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    The sporadic second Janko group $J_2$ is generated by an element of order two and one of order three and hence is a quotient of the modular group $PSL_2(\mathbb{Z}) = C_2 \ast C_3$. This Janko group has a 100-dimensional permutation representation and hence there is an index 100 subgroup $G$ of the modular group such… Read more »

  • math, number theory

    Aaron Siegel on transfinite number hacking

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    One of the coolest (pure math) facts in Conway’s book ONAG is the explicit construction of the algebraic closure $\overline{\mathbb{F}_2}$ of the field with two elements as the set of all ordinal numbers smaller than $(\omega^{\omega})^{\omega}$ equipped with nimber addition and multiplication. Some time ago we did run a couple of posts on this. In… Read more »

  • absolute, math, number theory

    Quiver Grassmannians and $\mathbb{F}_1$-geometry

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    Reineke’s observation that any projective variety can be realized as a quiver Grassmannian is bad news: we will have to look at special representations and/or dimension vectors if we want the Grassmannian to have desirable properties. Some people still see a silver lining: it can be used to define a larger class of geometric objects… Read more »

  • web

    bookworm arXiv

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    One of the nicer tools around is bookworm arXiv which ‘is a collaboration between the Harvard Cultural Observatory, arxiv.org, and the Open Science Data Cloud. It enables you to explore lexical trends in over 700,000 e-prints, spanning mathematics, physics, computer science, and statistics’ posted on the arXiv. One possible use is to explore the popularity… Read more »

  • web

    the matrix reloaded

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    The dinosaurs among you may remember that before this blog we had the ‘na&g-forum’ to accompany our master-class in noncommutative algebra & geometry. That forum ran on an early flat-panel iMac G4 which was, for lack of a better name, baptized ‘the matrix’. The original matrix did survive the unification of the three Antwerp universities… Read more »

  • math, noncommutative

    noncommutative geometry at the Lorentz center

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    This week i was at the conference Noncommutative Algebraic Geometry and its Applications to Physics at the Lorentz center in Leiden. It was refreshing to go to a conference where i knew only a handful of people beforehand and where everything was organized to Oberwolfach perfection. Perhaps i’ll post someday on some of the (to… Read more »

  • absolute, math, noncommutative

    Manin’s three-space-2000

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    Almost three decades ago, Yuri Manin submitted the paper “New dimensions in geometry” to the 25th Arbeitstagung, Bonn 1984. It is published in its proceedings, Springer Lecture Notes in Mathematics 1111, 59-101 and there’s a review of the paper available online in the Bulletin of the AMS written by Daniel Burns. In the introduction Manin… Read more »

  • groups, math

    Monsters and Moonshine : a booklet

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    I’ve LaTeXed $48=2 \times 24$ posts into a 114 page booklet Monsters and Moonshine for you to download. The $24$ ‘Monsters’ posts are (mostly) about finite simple (sporadic) groups : we start with the Scottish solids (hoax?), move on to the 14-15 game groupoid and a new Conway $M_{13}$-sliding game which uses the sporadic Mathieu… Read more »

  • math

    The martial art of giving talks

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    Last fall, Matilde Marcolli gave a course at CalTech entitled Oral Presentation: The (Martial) Art of Giving Talks. The purpose of this course was to teach students “how to effectively communicate their work in seminars and conferences and how to defend it from criticism from the audience”. The lecture notes contain basic information on the… Read more »

  • noncommutative, stories

    how noncommutative geometry shot itself

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    I’ve never apologized for prolonged periods of blogsilence and have no intention to start now. But, sometimes you need to expose the things holding you back before you can turn the page and (hopefully) start afresh. Long time readers of this blog know I’ve often warned against group-think, personality cults and the making of exaggerate… Read more »

  • absolute, noncommutative

    Prep-notes dump

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    Here are the scans of my crude prep-notes for some of the later seminar-talks. These notes still contain mistakes, most of them were corrected during the talks. So, please, read these notes with both mercy are caution! Hurwitz formula imples ABC : The proof of Smirnov’s argument, but modified so that one doesn’t require an… Read more »

  • absolute

    On aliens and reality

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    October 21st : Dear Diary, today’s seminar was fun, though a bit unconventional. The intention was to explain faithfully flat descent, but at the last moment i had the crazy idea to let students discover the main idea themselves (in the easiest of examples) by means of this thought experiment : “I am an alien,… Read more »

  • absolute

    meanwhile, at angs+

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    We’ve had three seminar-sessions so far, and the seminar-blog ‘angs+’ contains already 20 posts and counting. As blogging is not a linear activity, I will try to post here at regular intervals to report on the ground we’ve covered in the seminar, providing links to the original angs+ posts. This year’s goal is to obtain… Read more »

  • stories

    #cestGrothendieck

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    In Belgium the hashtag-craze of the moment is #cestjoelle. Joelle Milquet is perceived to be the dark force behind everything, from the crisis in Greece, over DSK, to your mother-in-law coming over this weekend? #cestjoelle. Sam Leith used the same meme in his book the coincidence engine. A hurricane assembling a passenger jet out of… Read more »

  • absolute, noncommutative, web

    3 related new math-sites

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    F_un Mathematics Hardly a ‘new’ blog, but one that is getting a new life! On its old homepage you’ll find a diagonal banner stating ‘This site has moved’ and clicking on it will guide you to its new location : cage.ugent.be/~kthas/Fun. From now on, this site will be hosted at the University of Ghent and… Read more »