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	<title>Concrete Nonsense</title>
	<link>http://concretenonsense.wordpress.com</link>
	<description>A group blog about mathematics</description>
	<lastBuildDate>Mon, 09 Nov 2009 15:30:58 +0000</lastBuildDate>
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	<item>
		<title>Chow rings and K-theory</title>
		<description><![CDATA[I want to write a post about the set-valued tableaux of Buch and how they are related to Schur polynomials. But since these two things are related to the K-theory and Chow ring, respectively, of the Grassmannian, I thought I would write a post explaining some basic generalities between the Chow ring and K-theory. Let [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=concretenonsense.wordpress.com&blog=2918042&post=758&subd=concretenonsense&ref=&feed=1" />]]></description>
		<link>http://concretenonsense.wordpress.com/2009/11/09/chow-rings-and-k-theory/</link>
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		<title>Exceptional sequences for the Grassmannian</title>
		<description><![CDATA[Let K be a field of characteristic 0, and let V be a vector space over K of dimension n, and pick k &#60; n. Let X be the Grassmannian Grass(k, V). We&#8217;ll briefly explore the (bounded) derived category of coherent sheaves of X, denoted .
1. Derived category review
For those unfamiliar with derived categories, here&#8217;s [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=concretenonsense.wordpress.com&blog=2918042&post=733&subd=concretenonsense&ref=&feed=1" />]]></description>
		<link>http://concretenonsense.wordpress.com/2009/10/26/exceptional-sequences-for-the-grassmannian/</link>
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		<title>GLFq III: characteristic map</title>
		<description><![CDATA[In the last post of this series, I gave some definitions and facts regarding the Hall&#8211;Littlewood functions. I also sketched the relationship between symmetric functions and representations of the symmetric group. Now we&#8217;ll see how this works for the finite general linear groups.
We want to imitate the Frobenius character that is used to relate the [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=concretenonsense.wordpress.com&blog=2918042&post=710&subd=concretenonsense&ref=&feed=1" />]]></description>
		<link>http://concretenonsense.wordpress.com/2009/10/12/glfq-iii-characteristic-map/</link>
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		<title>A Free Association On Basic Adjoints</title>
		<description><![CDATA[I&#8217;ve been betraying the title of this blog and doing some abstract nonsense lately, mostly to relearn algebraic geometry for the -th time for some embarrassingly large . With the memory capabilities of a muffin, I am practically starting over each time. Luckily, each adventure feels slightly more beatable (exp points?), since I have a [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=concretenonsense.wordpress.com&blog=2918042&post=713&subd=concretenonsense&ref=&feed=1" />]]></description>
		<link>http://concretenonsense.wordpress.com/2009/10/02/a-free-association-on-basic-adjoints/</link>
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		<title>GLFq II: Hall&#8211;Littlewood functions</title>
		<description><![CDATA[Last time, I discussed how to parametrize the conjugacy classes of the general linear group G over a finite field. In a sense, this group is a q-analogue of the symmetric group, so we might try to imitate the constructions for the symmetric group to get information about G. There&#8217;s a nice construction that Frobenius [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=concretenonsense.wordpress.com&blog=2918042&post=684&subd=concretenonsense&ref=&feed=1" />]]></description>
		<link>http://concretenonsense.wordpress.com/2009/09/28/glfq-ii-hall-littlewood-functions/</link>
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		<title>GLFq I: Conjugacy classes of a finite general linear group</title>
		<description><![CDATA[I&#8217;d like to start a series of posts, GLFq (general linear group over a finite field), in which I hope to explain the representation theory of  (n and q will remain fixed). In this first post, I&#8217;ll explain how to write down the conjugacy classes of G. In later posts, I plan to introduce [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=concretenonsense.wordpress.com&blog=2918042&post=665&subd=concretenonsense&ref=&feed=1" />]]></description>
		<link>http://concretenonsense.wordpress.com/2009/09/14/glfq-i-conjugacy-classes-of-a-finite-general-linear-group/</link>
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		<title>Symplectic geometry II</title>
		<description><![CDATA[Back to symplectic geometry. So far, everything I did in my last post only used the fact that the symplectic form  was skew symmetric, not that it was closed. Indeed the &#8220;closed&#8221; property is rather mysterious, (as far as I&#8217;m concerned, although in the literature it is called &#8220;geometric&#8221;), since I don&#8217;t know of [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=concretenonsense.wordpress.com&blog=2918042&post=661&subd=concretenonsense&ref=&feed=1" />]]></description>
		<link>http://concretenonsense.wordpress.com/2009/09/03/symplectic-geometry-ii/</link>
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		<title>Symplectic geometry I</title>
		<description><![CDATA[One of my summer projects was to try to learn symplectic geometry. In this, my first installment of notes, I discuss some introductory notions; hopefully it&#8217;s not too rambling. In the continuation, I&#8217;ll prove Darboux&#8217;s theorem, a fundamental result which says that locally, all symplectic spaces are isomorphic (something which sharply distinguishes symplectic geometry from [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=concretenonsense.wordpress.com&blog=2918042&post=638&subd=concretenonsense&ref=&feed=1" />]]></description>
		<link>http://concretenonsense.wordpress.com/2009/09/02/638/</link>
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		<title>A Fock space representation</title>
		<description><![CDATA[Lately I&#8217;ve been reading about quantum groups. I particularly enjoyed Bernard Leclerc&#8217;s paper Symmetric functions and the Fock space representation of , so I want to discuss a little bit of it. In particular, I want to give an example of the technique of deforming an object in order to see &#8220;hidden structure.&#8221; My notation [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=concretenonsense.wordpress.com&blog=2918042&post=623&subd=concretenonsense&ref=&feed=1" />]]></description>
		<link>http://concretenonsense.wordpress.com/2009/08/31/a-fock-space-representation/</link>
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		<title>Trees, The BEST Theorem, and Alexander Polynomials</title>
		<description><![CDATA[Most of my &#8220;free math time&#8221; has been used to study for quals, but today I&#8217;ve made myself post to stop Steven from taking over this blog.
One of my favorite elementary algebric combinatorial results is the Matrix Tree Theorem, which states:
In a nondirected graph with vertices labelled , the number of spanning trees is equal [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=concretenonsense.wordpress.com&blog=2918042&post=619&subd=concretenonsense&ref=&feed=1" />]]></description>
		<link>http://concretenonsense.wordpress.com/2009/08/20/trees-the-best-theorem-and-alexander-polynomials/</link>
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