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A. Varchenko

  1. Conformal blocks in the tensor product of vector representations and localization formulas.

    Wed, 11/18/2009 - 16:01 — SomNambul
    Authors: A. Varchenko, R. Rimanyi
    Subjects: Quantum Algebra
    Abstract

    Using equivariant localization formulas we give a formula for conformal
    blocks at level one on the sphere as suitable polynomials. Using this
    presentation we give a generating set in the space of conformal blocks at any
    level if the marked points on the sphere are generic.

  2. Path count asymptotics and Stirling numbers.

    Wed, 11/11/2009 - 16:01 — SomNambul
    Authors: A. Varchenko, K. Petersen
    Subjects: Combinatorics
    Abstract

    We obtain formulas for the growth rate of the numbers of certain paths in
    infinite graphs built on the two-dimensional Eulerian graph. Corollaries are
    identities relating Stirling numbers of the first and second kinds.

  3. Critical points and resonance of hyperplane arrangements.

    Wed, 11/04/2009 - 16:01 — SomNambul
    Authors: D. Cohen, G. Denham, M. Falk, A. Varchenko
    Subjects: Algebraic Geometry
    Abstract

    If F is a master function corresponding to a hyperplane arrangement A and a
    collection of weights y, we investigate the relationship between the critical
    set of F, the variety defined by the vanishing of the one-form w = d log F, and
    the resonance of y. For arrangements satisfying certain conditions, we show
    that if y is resonant in dimension p, then the critical set of F has
    codimension at most p. These include all free arrangements and all rank 3
    arrangements.

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