Tag: Galois

  • From the Da Vinci code to Galois

    In The Da Vinci Code, Dan Brown feels he need to bring in a French cryptologist, Sophie Neveu, to explain the mystery behind this series of numbers: 13 – 3 – 2 – 21 – 1 – 1 – 8 – 5 The Fibonacci sequence, 1-1-2-3-5-8-13-21-34-55-89-144-… is such that any number in it is the […]

  • the Reddit (after)effect

    Sunday january 2nd around 18hr NeB-stats went crazy. Referrals clarified that the post ‘What is the knot associated to a prime?’ was picked up at Reddit/math and remained nr.1 for about a day. Now, the dust has settled, so let’s learn from the experience. A Reddit-mention is to a blog what doping is to a…

  • Langlands versus Connes

    This is a belated response to a Math-Overflow exchange between Thomas Riepe and Chandan Singh Dalawat asking for a possible connection between Connes’ noncommutative geometry approach to the Riemann hypothesis and the Langlands program. Here’s the punchline : a large chunk of the Connes-Marcolli book Noncommutative Geometry, Quantum Fields and Motives can be read as…

  • Seating the first few thousand Knights

    The Knight-seating problems asks for a consistent placing of n-th Knight at an odd root of unity, compatible with the two different realizations of the algebraic closure of the field with two elements.

  • big Witt vectors for everyone (1/2)

    Next time you visit your math-library, please have a look whether these books are still on the shelves : Michiel Hazewinkel‘s Formal groups and applications, William Fulton’s and Serge Lange’s Riemann-Roch algebra and Donald Knutson’s lambda-rings and the representation theory of the symmetric group. I wouldn’t be surprised if one or more of these books…

  • The odd knights of the round table

    Here’s a tiny problem illustrating our limited knowledge of finite fields : “Imagine an infinite queue of Knights ${ K_1,K_2,K_3,\ldots } $, waiting to be seated at the unit-circular table. The master of ceremony (that is, you) must give Knights $K_a $ and $K_b $ a place at an odd root of unity, say $\omega_a…

  • On2 : transfinite number hacking

    Surely Georg Cantor’s transfinite ordinal numbers do not have a real-life importance? Well, think again.

  • best of 2008 (1) : wiskundemeisjes

    A feeble attempt to translate the Marcolli-post by the ‘wiskundemeisjes’.

  • 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.

  • Manin’s geometric axis

    Manin proposes the idea of projecting spec(Z[x]) not only onto spec(Z), but also to a geometric axis by considering the integers as an algebra over the field with one element.