Tag: groups

  • eBook ‘geometry and the absolute point’ v0.1

    In preparing for next year’s ‘seminar noncommutative geometry’ I’ve converted about 30 posts to LaTeX, centering loosely around the topics students have asked me to cover : noncommutative geometry, the absolute point (aka the field with one element), and their relation to the Riemann hypothesis. The idea being to edit these posts thoroughly, add much […]

  • the birthday of the primes=knots analogy

    Last time we discovered that the mental picture to view prime numbers as knots in $S^3$ was first dreamed up by David Mumford. Today, we’ll focus on where and when this happened. 3. When did Mazur write his unpublished preprint? According to his own website, Barry Mazur did write the paper Remarks on the Alexander…

  • If Bourbaki=WikiLeaks then Weil=Assange

    In an interview with readers of the Guardian, December 3rd 2010, Julian Assange made a somewhat surprising comparison between WikiLeaks and Bourbaki, sorry, The Bourbaki (sic) : “I originally tried hard for the organisation to have no face, because I wanted egos to play no part in our activities. This followed the tradition of the…

  • Who dreamed up the primes=knots analogy?

    One of the more surprising analogies around is that prime numbers can be viewed as knots in the 3-sphere $S^3$. The motivation behind it is that the (etale) fundamental group of $\pmb{spec}(\mathbb{Z}/(p))$ is equal to (the completion) of the fundamental group of a circle $S^1$ and that the embedding $\pmb{spec}(\mathbb{Z}/(p)) \subset \pmb{spec}(\mathbb{Z})$ embeds this circle…

  • mathblogging and poll-results

    Mathblogging.org is a recent initiative and may well become the default starting place to check on the status of the mathematical blogosphere. Handy, if you want to (re)populate your RSS-aggregator with interesting mathematical blogs, is their graphical presentation of (nearly) all math-blogs ordered by type : group blogs, individual researchers, teachers and educators, journalistic writers,…

  • So, who did discover the Leech lattice?

    For the better part of the 30ties, Ernst Witt (1) did hang out with the rest of the ‘Noetherknaben’, the group of young mathematicians around Emmy Noether (3) in Gottingen. In 1934 Witt became Helmut Hasse‘s assistent in Gottingen, where he qualified as a university lecturer in 1936. By 1938 he has made enough of…

  • Who discovered the Leech lattice?

    The Leech lattice was, according to wikipedia, ‘originally discovered by Ernst Witt in 1940, but he did not publish his discovery’ and it ‘was later re-discovered in 1965 by John Leech’. However, there is very little evidence to support this claim. The facts What is certain is that John Leech discovered in 1965 an amazingly…

  • Seriously now, where was the Bourbaki wedding?

    A few days before Halloween, Norbert Dufourcq (who died december 17th 1990…), sent me a comment, containing lots of useful information, hinting I did get it wrong about the church of the Bourbali wedding in the previous post. Norbert Dufourcq, an organist and student of Andre Machall, the organist-in-charge at the Saint-Germain-des-Prés church in 1939,…

  • Conway’s big picture

    Conway and Norton showed that there are exactly 171 moonshine functions and associated two arithmetic subgroups to them. We want a tool to describe these and here’s where Conway’s big picture comes in very handy. All moonshine groups are arithmetic groups, that is, they are commensurable with the modular group. Conway’s idea is to view…

  • Mazur’s knotty dictionary

    The algebraic fundamental group of a scheme gives the Mazur-Kapranov-Reznikov dictionary between primes in number fields and knots in 3-manifolds.