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Krzysztof Oleszkiewicz

  1. On reverse hypercontractivity.

    Mon, 08/08/2011 - 15:01 — SomNambul
    Authors: Elchanan Mossel, Arnab Sen, Krzysztof Oleszkiewicz
    Subjects: Probability
    Abstract

    We study the notion of reverse hypercontractivity. We show that reverse
    hypercontractive inequalities are implied by standard hypercontractive
    inequalities as well as by the modified log-Sobolev inequality. Our proof is
    based on a new comparison lemma for Dirichlet forms and an extension of the
    Strook-Varapolos inequality.

  2. On the signatures of torus knots.

    Thu, 02/25/2010 - 16:01 — SomNambul
    Authors: Maciej Borodzik, Krzysztof Oleszkiewicz
    Subjects: Geometric Topology
    Abstract

    We study properties of the signature function of the torus knot $T_{p,q}$.
    First we provide a very elementary proof of the formula for the integral of the
    signatures over the circle. We obtain also a closed formula for the
    Tristram--Levine signature of a torus knot in terms of Dedekind sums.

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