Posts Categorized: representations

  • groups, number theory, representations

    Moonshine for everyone

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    Today, Samuel Dehority, Xavier Gonzalez, Neekon Vafa and Roger Van Peski arXived their paper Moonshine for all finite groups. Originally, Moonshine was thought to be connected to the Monster group. McKay and Thompson observed that the first coefficients of the normalized elliptic modular invariant \[ J(\tau) = q^{-1} + 196884 q + 21493760 q^2 +… Read more »

  • geometry, personal, rants, representations

    Stirring a cup of coffee

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    Please allow for a couple of end-of-semester bluesy ramblings. I just finished grading the final test of the last of five courses I lectured this semester. Most of them went, I believe, rather well. As always, it was fun to teach an introductory group theory course to second year physics students. Personally, I did enjoy… Read more »

  • 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, 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 »

  • geometry, groups, representations

    Klein’s dessins d’enfant and the buckyball

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    We saw that the icosahedron can be constructed from the alternating group $A_5 $ by considering the elements of a conjugacy class of order 5 elements as the vertices and edges between two vertices if their product is still in the conjugacy class. This description is so nice that one would like to have a… Read more »