Tag: geometry

  • 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 […]

  • Art and the absolute point (3)

    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…

  • Penrose tilings and noncommutative geometry

    Penrose tilings are aperiodic tilings of the plane, made from 2 sort of tiles : kites and darts. It is well known (see for example the standard textbook tilings and patterns section 10.5) that one can describe a Penrose tiling around a given point in the plane as an infinite sequence of 0’s and 1’s,…

  • 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…

  • Art and the absolute point (2)

    Last time we did recall Manin’s comparisons between some approaches to geometry over the absolute point $\pmb{spec}(\mathbb{F}_1)$ and trends in the history of art. In the comments to that post, Javier Lopez-Pena wrote that he and Oliver Lorscheid briefly contemplated the idea of extending Manin’s artsy-dictionary to all approaches they did draw on their Map…

  • Art and the absolute point

    In his paper Cyclotomy and analytic geometry over $\mathbb{F}_1$ Yuri I. Manin sketches and compares four approaches to the definition of a geometry over $\mathbb{F}_1$, the elusive field with one element. He writes : “Preparing a colloquium talk in Paris, I have succumbed to the temptation to associate them with some dominant trends in the…

  • Noncommutative algebra and geometry master-degree

    The lecturers, topics and dates of the 6 mini-courses in our ‘advanced master degree 2011 in noncommutative algebra and geometry’ are : February 21-25 Vladimir Bavula (University of Sheffield) : Localization Theory of Rings and Modules March 7-11 Hans-Jürgen Schneider (University of München) : Nichols Algebra and Root Systems April 11-12 Bernhard Keller (Université Paris…

  • 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,…

  • changes (ahead)

    In view or recents events & comments, some changes have been made or will be made shortly : categories : Sanitized the plethora of wordpress-categories to which posts belong. At the moment there are just 5 categories : ‘stories’ and ‘web’ (for all posts with low math-content) and three categories ‘level1’, ‘level2’ and ‘level3’, loosely…

  • Lists 2010 : MathOverflow bookmarks

    A few MathOverflow threads I bookmarked in 2010 for various reasons. Honest answer : Applications of algebraic geometry over a field with one element. James Borger’s answer : “I’m confident that the answer to the original question is no. There are hardly any theorems at all in the subject, much less ones with external applications!…