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Tuyen Trung Truong

  1. Degree complexity of birational maps related to matrix inversion: Symmetric case.

    Ср, 05/26/2010 - 15:01 — SomNambul
    Authors: Tuyen Trung Truong
    Subjects: Dynamical Systems
    Abstract

    For $q\geq 3$, we let $\mathcal{S}_q$ denote the projectivization of the set
    of symmetric $q\times q$ matrices with coefficients in $\mathbb{C}$. We let
    $I(x)=(x_{i,j})^{-1}$ denote the matrix inversion, and we let
    $J(x)=(x_{i,j}^{-1})$ be the matrix whose entries are the reciprocals of the
    entries of $x$. We let $K|\mathcal{S}_q=I\circ J:\mathcal{S}_q\rightarrow
    \mathcal{S}_q$ denote the restriction of the composition $I\circ J$ to
    $\mathcal{S}_q$. This is a birational map whose properties have attracted some
    attention in statistical mechanics.

  2. Local growth of pluri-subharmonic functions.

    Втр, 09/01/2009 - 12:47 — SomNambul
    Authors: Tuyen Trung Truong
    Subjects: Complex Variables
    Abstract

    We obtain some two-bound estimates for the local growth of pluri-subharmonic
    functions. We propose a conjecture which is similar to the comparison theorem
    in [H. Alexander and B. A. Taylor, Comparison of two capacities in
    $\mathbb{C}^n$, Math. Z. 186 (1984), 407--417]. We verify this conjecture in
    several cases. We then show that this conjecture implies extensions of the main
    result in [Alexander Brudnyi, Local inequalities for pluri-subharmonic
    functions, Annals Math. 149 (1999), No. 2, pp. 511--533]. In the appendix we
    give a new proof to that result of Brudnyi.

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