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Megumi Harada

  1. The equivariant K-theory of the affine Grassmannian of SU(2).

    Tue, 05/18/2010 - 15:01 — SomNambul
    Authors: Megumi Harada, Paul Selick, Lisa C. Jeffrey
    Subjects: Algebraic Topology
    Abstract

    Let $G=SU(2)$ and $\Omega G$ the space of based loops in SU(2). Motivated by
    the theory of Hamiltonian $LG$-spaces, we explicitly compute the topological
    equivariant $K$-theory $K_G^*(\Omega G)$ as an $R(G)$-module.

  2. A positive Monk formula in the S^1-equivariant cohomology of type A Peterson varieties.

    Wed, 08/26/2009 - 14:58 — SomNambul
    Authors: Megumi Harada, Julianna Tymoczko
    Subjects: Algebraic Geometry
    Abstract

    Peterson varieties are a special class of Hessenberg varieties that have been
    extensively studied e.g. by Peterson, Kostant, and Rietsch, in connection with
    the quantum cohomology of the flag variety. In this manuscript, we develop a
    generalized Schubert calculus, and in particular a positive Chevalley-Monk
    formula, for the ordinary and Borel-equivariant cohomology of the Peterson
    variety $Y$ in type $A_{n-1}$, with respect to a natural $S^1$-action arising
    from the standard action of the maximal torus on flag varieties.

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