Posts Categorized: noncommutative

  • books, geometry, noncommutative, representations

    let’s spend 3K on (math)books

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    Santa gave me 3000 Euros to spend on books. One downside: I have to give him my wish-list before monday. So, I’d better get started. Clearly, any further suggestions you might have will be much appreciated, either in the comments below or more directly via email. Today I’ll focus on my own interests: algebraic geometry,… Read more »

  • math, noncommutative

    A noncommutative moduli space

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    Supernatural numbers also appear in noncommutative geometry via James Glimm’s characterisation of a class of simple $C^*$-algebras, the UHF-algebras. A uniformly hyperfine (or, UHF) algebra $A$ is a $C^*$-algebra that can be written as the closure, in the norm topology, of an increasing union of finite-dimensional full matrix algebras $M_{c_1}(\mathbb{C}) \subset M_{c_2}(\mathbb{C}) \subset … \quad… Read more »

  • math, noncommutative, representations

    Quiver Grassmannians can be anything

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    A standard Grassmannian $Gr(m,V)$ is the manifold having as its points all possible $m$-dimensional subspaces of a given vectorspace $V$. As an example, $Gr(1,V)$ is the set of lines through the origin in $V$ and therefore is the projective space $\mathbb{P}(V)$. Grassmannians are among the nicest projective varieties, they are smooth and allow a cell… 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 »

  • 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, 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 »

  • noncommutative

    Penrose tilings and noncommutative geometry

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    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,… Read more »

  • noncommutative, web

    Noncommutative algebra and geometry master-degree

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    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… Read more »

  • noncommutative

    On the Reality of Noncommutative Space

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    Guest post by Fred Van Oystaeyen. In my book “Virtual Topology and Functorial Geometry” (Taylor and Francis, 2009) I proposed a noncommutative version of space-time ; it is a toy model, but mathematically correct and I included a few philosophical remarks about : “What if reality is noncommutative ?”. I want to add a few… Read more »

  • absolute, noncommutative, number theory

    Seating the first few billion Knights

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    The odd Knight of the round table problem asks for a consistent placement of the n-th Knight in the row at an odd root of unity, compatible with the two different realizations of the algebraic closure of the field with two elements. The first identifies the multiplicative group of its non-zero elements with the group… Read more »

  • noncommutative, web

    Jason & David, the Ninja warriors of noncommutative geometry

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    SocialMention gives a rather accurate picture of the web-buzz on a specific topic. For this reason I check it irregularly to know what’s going on in noncommutative geometry, at least web-wise. Yesterday, I noticed two new kids on the block : Jason and David. Their blogs have (so far ) 44 resp. 27 posts, this… Read more »

  • noncommutative, web

    Grothendieck’s folly

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    Never a dull moment with Books Ngram Viewer. Pick your favorite topic(s) and try to explain and name valleys and peaks in the Ngram. An example. I wanted to compare the relative impact of a couple of topics I love, algebraic geometry (blue), category theory (red), representation theory (green) and noncommutative geometry (the bit of… 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 »

  • noncommutative

    noncommutative space quiz

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    Creating (or taking) an image and explaining how it depicts your mental picture of a noncommutative space is one thing. Ideally, the image should be strong enough so that other people familiar with it might have a reasonable guess what you attempt to depict. But, is there already enough concordance in our views of noncommutative… Read more »

  • absolute, geometry, noncommutative

    Connes & Consani go categorical

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    Today, Alain Connes and Caterina Consani arXived their new paper Schemes over $ \mathbb{F}_1$ and zeta functions. It is a follow-up to their paper On the notion of geometry over $ \mathbb{F}_1$, which I’ve tried to explain in a series of posts starting here. As Javier noted already last week when they updated their first… Read more »

  • geometry, noncommutative

    noncommutative F_un geometry (2)

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    We use Kontsevich’s idea of thin varieties to define complexified varieties over F\_un.

  • 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.

  • groups, noncommutative

    Monstrous frustrations

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    Thanks for clicking through… I guess. If nothing else, it shows that just as much as the stock market is fueled by greed, mathematical reasearch is driven by frustration (or the pleasure gained from knowing others to be frustrated). I did spend the better part of the day doing a lengthy, if not laborious, calculation,… Read more »