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2012 Fiscal Year Final Research Report

Formal KZ equation on moduli spaces and multiple polylogarithms

Research Project

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Project/Area Number 22540035
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionWaseda University

Principal Investigator

UENO Kimio  早稲田大学, 理工学術院, 教授 (70160190)

Project Period (FY) 2010 – 2012
KeywordsKZ 方程式 / モジュライ空間 / 多重対数関数 / 多重ゼータ値 / リーマン : ヒルベルト問題
Research Abstract

The paper entitled by ”KZ equation on the moduli space M_{0,5} and the harmonic product of multiple polylogarithms” appeared in Proc. London. Math. Soc.. In this article, we established the algebraic foundation such as the reduced bar algebra, and the geometric foundation such as the fiber space structure of the moduli space M_{0,5}, and showed the decomposition theorem of the fundamental solution of the KZ equation on M_{0.5}. Moreover we showed that the decomposition theorem is equivalent to the generalized harmonic product relations, and that they involve all the harmonic products of multiple polylogarithms of one variable. The paper entitled by ‘’The Inversion Formula of Polylogarithms abd the Riemann-Hilbert Problem” also was published last year. In this paper, we succeeded in characterzing polylogarithms by using the Riemann-Hilbert problem under a certain asymptotic condition.

  • Research Products

    (4 results)

All 2013 2012

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (2 results)

  • [Journal Article] TheInversion Formula of Polylogarithms and the Rieman-Hilbert Problem2013

    • Author(s)
      Shu Oi and Kimio Ueno
    • Journal Title

      Springer Proceedings in Mathematics and Statistics

      Volume: 40 Pages: 491-496

    • Peer Reviewed
  • [Journal Article] KZ equation on the moduli space M_{0,5} and the harmonic product of multiple polylogarithms2012

    • Author(s)
      Shu Oi and Kimio Ueno
    • Journal Title

      Proc.London Math. Acad.

      Volume: (3) 105 Pages: 983-1020

    • Peer Reviewed
  • [Presentation] 1 変数KZ 方程式の接続問題とRiemann-Hilbert 問題2013

    • Author(s)
      大井周-上野喜三雄
    • Organizer
      日本数学会年会
    • Place of Presentation
      京都大学吉田キャンパス
    • Year and Date
      2013-03-23
  • [Presentation] 2 重対数関数の6角形関係式とRiemann-Hilbert 問題2013

    • Author(s)
      大井周-上野喜三雄
    • Organizer
      日本数学会年会
    • Place of Presentation
      京都大学吉田キャンパス
    • Year and Date
      2013-03-23

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Published: 2014-08-29  

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