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Alexander Stolin

  1. Kervaire and Murthy conjecture and Ullom's inequality.

    Wed, 03/10/2010 - 16:01 — SomNambul
    Authors: Alexander Stolin
    Subjects: Number Theory
    Abstract

    We study the cyclotomic field of $p^n$ roots of unity and the Sylow
    p-component of its class group. Here p is a semi-regular prime. We prove that
    for $n\geq 2$ the number of generators is equal to the corresponding Iwasawa
    number $\lambda$.

  2. Poisson structures compatible with the cluster algebra structure in Grassmannians.

    Thu, 09/03/2009 - 17:38 — SomNambul
    Authors: Michael Gekhtman, Michael Shapiro, Alexander Stolin, Alek Vainshtein
    Subjects: Quantum Algebra
    Abstract

    We describe all Poisson brackets compatible with the natural cluster algebra
    structure in the open Schubert cell of the Grassmannian $G_k(n)$ and show that
    any such bracket endows $G_k(n)$ with a structure of a Poisson homogeneous
    space with respect to the natural action of $SL_n$ equipped with an R-matrix
    Poisson-Lie structure. The corresponding R-matrices belong to the simplest
    class in the Belavin-Drinfeld classification. Moreover, every compatible
    Poisson structure can be obtained this way.

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