Posts Tagged: noncommutative

  • 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 »

  • 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 »

  • 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 »

  • 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 »

  • web

    mathblogging and poll-results

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    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,… 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 »

  • web

    changes (ahead)

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    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… 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 »

  • web

    Books Ngram for your upcoming parties

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    No christmas- or new-years family party without heated discussions. Often on quite silly topics. For example, which late 19th-century bookcharacter turned out to be most influential in the 20th century? Dracula, from the 1897 novel by Irish author Bram Stoker or Sir Arthur Conan Doyle’s Sherlock Holmes who made his first appearance in 1887? Well,… 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 »

  • web

    introducing : the n-geometry cafe

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    It all started with this comment on the noncommutative geometry blog by “gabriel” : Even though my understanding of noncommutative geometry is limited, there are some aspects that I am able to follow. I was wondering, since there are so few blogs here, why don’t you guys forge an alliance with neverending books, you blog… Read more »

  • stories

    Bourbakism & the queen bee syndrome

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    Probably the smartest move I’ve made after entering math-school was to fall in love with a feminist. Yeah well, perhaps I’ll expand a bit on this sentence another time. For now, suffice it to say that I did pick up a few words in the process, among them : the queen bee syndrome : women… Read more »

  • web

    Now here’s an idea

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    Boy, do I feel stupid for having written close to 500 blog-posts hoping (in vain) they might eventually converge into a book project… Gil Kalai is infinitely smarter. Get a fake gmail account, invent a fictitious character and start COMMENTING and provoking responses. That’s how “Gina” appeared on the scene, cut and pasted her comments… 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 »

  • featured

    Pollock your own noncommutative space

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    I really like Matilde Marcolli’s idea to use some of Jackson Pollock’s paintings as metaphors for noncommutative spaces. In her talk she used this painting and refered to it (as did I in my post) as : Jackson Pollock “Untitled N.3”. Before someone writes a post ‘The Pollock noncommutative space hoax’ (similar to my own… Read more »

  • featured

    Views of noncommutative spaces

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    The general public expects pictures from geometers, even from non-commutative geometers. Hence, it is important for researchers in this topic to make an attempt to convey the mental picture they have of their favourite noncommutative space, … somehow. Two examples : This picture was created by Shahn Majid. It appears on his visions of noncommutative… Read more »

  • web

    yet another math2.0 proposal

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    Tim Gowers’ dream of massively collaborative mathematics got me thinking…

  • featured

    Mumford’s treasure map

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    In the series “Brave new geometries” we give an introduction to ‘strange’ but exciting new ideas. We start with Grothendieck’s scheme-revolution, go on with Soule’s geometry over the field with one element, Mazur’s arithmetic topology, Grothendieck’s anabelian geometry, Connes’ noncommutative geometry etc.

  • 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.

  • absolute, web

    This week at F_un Mathematics (1)

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    Some links to posts on Soule’s algebraic geometry over the field with one element.

  • featured

    Connes-Consani for undergraduates (3)

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    A quick recap of last time. We are trying to make sense of affine varieties over the elusive field with one element $\mathbb{F}_1 $, which by Grothendieck’s scheme-philosophy should determine a functor $\mathbf{nano}(N)~:~\mathbf{abelian} \rightarrow \mathbf{sets} \qquad A \mapsto N(A) $ from finite Abelian groups to sets, typically giving pretty small sets $N(A) $. Using the… Read more »