Posts Tagged: Riemann

  • absolute, web

    eBook ‘geometry and the absolute point’ v0.1

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    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… Read more »

  • stories

    Art and the absolute point (3)

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    Previously, we have recalled comparisons between approaches to define a geometry over the absolute point and art-historical movements, first those due to Yuri I. Manin, subsequently some extra ones due to Javier Lopez Pena and Oliver Lorscheid. In these comparisons, the art trend appears to have been chosen more to illustrate a key feature of… Read more »

  • stories

    the Reddit (after)effect

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    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… Read more »

  • stories, web

    NeB : 7 years and now an iPad App

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    Exactly 7 years ago I wrote my first post. This blog wasn’t called NeB yet and it used pMachine, a then free blogging tool (later transformed into expression engine), rather than WordPress. Over the years NeB survived three hardware-upgrades of ‘the Matrix’ (the webserver hosting it), more themes than I care to remember, and a… Read more »

  • noncommutative, number theory

    Langlands versus Connes

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    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… Read more »

  • absolute

    big Witt vectors for everyone (1/2)

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    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… Read more »

  • groups

    looking for the moonshine picture

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    We have seen that Conway’s big picture helps us to determine all arithmetic subgroups of $PSL_2(\mathbb{R}) $ commensurable with the modular group $PSL_2(\mathbb{Z}) $, including all groups of monstrous moonshine. As there are exactly 171 such moonshine groups, they are determined by a finite subgraph of Conway’s picture and we call the minimal such subgraph… Read more »

  • web

    best of 2008 (2) : big theorems

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    A comment to Charles Siegel’s ‘big theorems’-series got me checking my stats.

  • geometry, number theory, stories

    Andre Weil on the Riemann hypothesis

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    Some quotes of Andre Weil on the Riemann hypothesis.

  • absolute, geometry, noncommutative

    noncommutative F_un geometry (1)

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    We propose to extend the Connes-Consani definition to noncommuntative F_un varieties.

  • featured

    what does the monster see?

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    The Monster is the largest of the 26 sporadic simple groups and has order 808 017 424 794 512 875 886 459 904 961 710 757 005 754 368 000 000 000 = 2^46 3^20 5^9 7^6 11^2 13^3 17 19 23 29 31 41 47 59 71. It is not so much the size… Read more »

  • web

    GAMAP 2008

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    Next week, our annual summer school Geometric and Algebraic Methods with Applications in Physics will start, once again (ive lost count which edition it is). Because Isar is awol to la douce France, I’ll be responsible (once again) for the web-related stuff of the meeting. So, here a couple of requests to participants/lecturers : if… Read more »

  • geometry, groups, number theory

    the buckyball curve

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    We are after the geometric trinity corresponding to the trinity of exceptional Galois groups The surfaces on the right have the corresponding group on the left as their group of automorphisms. But, there is a lot more group-theoretic info hidden in the geometry. Before we sketch the $L_2(11) $ case, let us recall the simpler… Read more »

  • geometry, groups, representations

    Klein’s dessins d’enfant and the buckyball

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    We saw that the icosahedron can be constructed from the alternating group $A_5 $ by considering the elements of a conjugacy class of order 5 elements as the vertices and edges between two vertices if their product is still in the conjugacy class. This description is so nice that one would like to have a… Read more »

  • geometry, groups

    the buckyball symmetries

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    The buckyball is without doubt the hottest mahematical object at the moment (at least in Europe). Recall that the buckyball (middle) is a mixed form of two Platonic solids the Icosahedron on the left and the Dodecahedron on the right. For those of you who don’t know anything about football, it is that other ball-game,… Read more »

  • absolute

    Looking for F_un

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    There are only a handful of human activities where one goes to extraordinary lengths to keep a dream alive, in spite of overwhelming evidence : religion, theoretical physics, supporting the Belgian football team and … mathematics. In recent years several people spend a lot of energy looking for properties of an elusive object : the… Read more »

  • stories

    New world record obscurification

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    I’ve always thought of Alain Connes as the unchallengeable world-champion opaque mathematical writing, but then again, I was proven wrong. Alain’s writings are crystal clear compared to the monstrosity the AMS released to the world : In search of the Riemann zeros – Strings, fractal membranes and noncommutative spacetimes by Michel L. Lapidus. Here’s a… Read more »

  • featured

    KMS, Gibbs & zeta function

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    Time to wrap up this series on the Bost-Connes algebra. Here’s what we have learned so far : the convolution product on double cosets $\begin{bmatrix} 1 & \mathbb{Z} \\ 0 & 1 \end{bmatrix} \backslash \begin{bmatrix} 1 & \mathbb{Q} \\ 0 & \mathbb{Q}_{> 0} \end{bmatrix} / \begin{bmatrix} 1 & \mathbb{Z} \\ 0 & 1 \end{bmatrix} $… Read more »

  • featured

    music of the primes (1)

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    This semester, I’m running a 3rd year course on Marcus du Sautoy’s The music of the primes. The concept being that students may suggest topics, merely sketched in the book, and then we’ll go a little deeper into them. I’ve been rather critical about the book before, but, rereading it last week (and knowing a… Read more »

  • stories

    vacation reading (2)

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    Vacation is always a good time to catch up on some reading. Besides, there’s very little else you can do at night in a ski-resort… This year, I’ve taken along The Archimedes Codex: Revealing The Secrets Of The World’s Greatest Palimpsest by Reviel Netz and William Noel telling the story of the Archimedes Palimpsest. The… Read more »

  • stories

    un-doing the Grothendieck?

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    (via the Arcadian Functor) At the time of the doing the Perelman-post someone rightfully commented that “making a voluntary retreat from the math circuit to preserve one’s own well-being (either mental, physical, scientific …)” should rather be called doing the Grothendieck as he was the first to pull this stunt. On Facebook a couple of… Read more »

  • featured

    the Bost-Connes coset space

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    In the series “Noncommutative geometry and the Riemann zeta function” we give an introduction to the Bost-Connes algebra. We describe its relation to adeles/ideles and to KMS-states leading to the zeta-function as the partition function.

  • stories

    now what?

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    You may not have noticed, but the really hard work was done behind the scenes, resurrecting about 300 old posts (some of them hidden by giving them ‘private’-status). Ive only deleted about 10 posts with little or no content and am sorry I’ve self-destructed about 20-30 hectic posts over the years by pressing the ‘delete… Read more »

  • stories

    mathematics for 2008 (and beyond)

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    Via the n-category cafe (and just now also the Arcadian functor ) I learned that Benjamin Mann of DARPA has constructed a list of 23 challenges for mathematics for this century. DARPA is the “Defense Advanced Research Projects Agency” and is an agency of the United States Department of Defense ‘responsible for the development of… Read more »

  • featured

    recycled : dessins

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    In a couple of days I’ll be blogging for 4 years… and I’m in the process of resurrecting about 300 posts from a database-dump made in june. For example here’s my first post ever which is rather naive. This conversion program may last for a couple of weeks and I apologize for all unwanted pingbacks… Read more »