Posts Tagged: moduli

  • rants, stories

    what have quivers done to students?

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    A few years ago a student entered my office asking suggestions for his master thesis. “I’m open to any topic as long as it has nothing to do with those silly quivers!” At that time not the best of opening-lines to address me and, inevitably, the most disastrous teacher-student-conversation-ever followed (also on my part, i’m… 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 »

  • 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 »

  • featured

    neverendingbooks-geometry (2)

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    Here pdf-files of older NeverEndingBooks-posts on geometry. For more recent posts go here.

  • stories

    down with determinants

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    The categorical cafe has a guest post by Tom Leinster Linear Algebra Done Right on the book with the same title by Sheldon Axler. I haven’t read the book but glanced through his online paper Down with determinants!. Here is ‘his’ proof of the fact that any n by n matrix A has at least… Read more »

  • stories

    THE rationality problem

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    This morning, Esther Beneish arxived the paper The center of the generic algebra of degree p that may contain the most significant advance in my favourite problem for over 15 years! In it she claims to prove that the center of the generic division algebra of degree p is stably rational for all prime values… Read more »

  • web

    2006 paper nominees

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    Here are my nominees for the 2006 paper of the year award in mathematics & mathematical physics : in math.RA : math.RA/0606241 : Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I by Maxim Kontsevich and Yan Soibelman. Here is the abstract : We develop geometric approach to A-infinity algebras and A-infinity categories based… Read more »

  • web

    MyLife@300dpi

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    Three years ago I did spend three weeks next to my Canonscan, painstakingly scanning all individual pages of every preprint I ever wrote. Next, I converted every page to PDF, resized it (in order to control the size) and bundled them into PDF-files. A typical preprint would take me roughly three quarters of an hour… Read more »

  • featured

    noncommutative topology (3)

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    For finite dimensional hereditary algebras, one can describe its noncommutative topology (as developed in part 2) explicitly, using results of Markus Reineke in The monoid of families of quiver representations. Consider a concrete example, say $A = \begin{bmatrix} \mathbb{C} & V \\ 0 & \mathbb{C} \end{bmatrix}$ where $V$ is an n-dimensional complex vectorspace, or equivalently,… Read more »

  • stories

    hectic days

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    Hectic days ahead! Today, there is the Ph.D. defense of Stijn Symens and the following two days there is a meeting in Ghent where Jacques Alev and me organize a special session on non-commutative algebra. Here is the programme of that section Session 1 (Friday 20 May) — chair : Jacques Alev (Univ. Reims) 15.30-16.25… Read more »

  • stories

    reading backlog

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    One of the things I like most about returning from a vacation is to have an enormous pile of fresh reading : a week's worth of newspapers, some regular mail and much more email (three quarters junk). Also before getting into bed after the ride I like to browse through the arXiv in search for… Read more »

  • featured

    hyper-resolutions

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    [Last time][1] we saw that for $A$ a smooth order with center $R$ the Brauer-Severi variety $X_A$ is a smooth variety and we have a projective morphism $X_A \rightarrow \mathbf{max}~R$ This situation is very similar to that of a desingularization $~X \rightarrow \mathbf{max}~R$ of the (possibly singular) variety $~\mathbf{max}~R$. The top variety $~X$ is a… Read more »

  • featured

    cotangent bundles

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    The previous post in this sequence was [moduli spaces][1]. Why did we spend time explaining the connection of the quiver $Q~:~\xymatrix{\vtx{} \ar[rr]^a & & \vtx{} \ar@(ur,dr)^x} $ to moduli spaces of vectorbundles on curves and moduli spaces of linear control systems? At the start I said we would concentrate on its _double quiver_ $\tilde{Q}~:~\xymatrix{\vtx{} \ar@/^/[rr]^a… Read more »

  • featured

    moduli spaces

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    In [the previous part][1] we saw that moduli spaces of suitable representations of the quiver $\xymatrix{\vtx{} \ar[rr] & & \vtx{} \ar@(ur,dr)} $ locally determine the moduli spaces of vectorbundles over smooth projective curves. There is yet another classical problem related to this quiver (which also illustrates the idea of looking at families of moduli spaces… Read more »

  • featured

    representation spaces

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    The previous part of this sequence was [quiver representations][1]. When $A$ is a formally smooth algebra, we have an infinite family of smooth affine varieties $\mathbf{rep}_n~A$, the varieties of finite dimensional representations. On $\mathbf{rep}_n~A$ there is a basechange action of $GL_n$ and we are really interested in _isomorphism classes_ of representations, that is, orbits under… Read more »

  • stories

    driven by ambition and sloth

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    Here’s a part of yesterday’s post by bitch ph.d. : But first of all I have to figure out what the hell I’m going to teach my graduate students this semester, and really more to the point, what I am not going to bother to try to cram into this class just because it’s my… Read more »

  • featured

    nog course outline

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    Now that the preparation for my undergraduate courses in the first semester is more or less finished, I can begin to think about the courses I’ll give this year in the master class non-commutative geometry. For a change I’d like to introduce the main ideas and concepts by a very concrete example : Ginzburg’s coadjoint-orbit… Read more »

  • featured

    NOG master class

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    Yesterday I made reservations for lecture rooms to run the master class on non-commutative geometry sponsored by the ESF-NOG project. We have a lecture room on monday- and wednesday afternoon and friday the whole day which should be enough. I will run two courses in the program : non-commutative geometry and projects in non-commutative geometry… Read more »