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2011 Fiscal Year Final Research Report

Various aspects of hyperplane arrangements

Research Project

  • PDF
Project/Area Number 21340001
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

TERAO Hiroaki  北海道大学, 大学院・理学研究院, 教授 (90119058)

Project Period (FY) 2009 – 2011
Keywords代数的組合せ論 / 超平面配置
Research Abstract

The definition of hyperplane arrangements is, like groups and rings, deceptively simple but they are not simplistic objects. In the first year of this research project, we successfully constructed a research network encompassing specialties and generations in order to understand diversified viewpoints of hyperplane arrangements in a wide spectrum and to hold a commanding position for advancing the research. Consequently, we studied the subject from various viewpoints including combinatorics, algebraic geometry, group theory, Lie algebra theory and statistics and described their mutual relations. The most conspicuous example is the relationship between the Weyl arrangements and the Bernoulli polynomials, which was discovered by us in 2010. It has been scrutinized and expected to develop further.

  • Research Products

    (20 results)

All 2012 2011 2010 2009 Other

All Journal Article (9 results) (of which Peer Reviewed: 9 results) Presentation (6 results) Book (3 results) Remarks (2 results)

  • [Journal Article] Equivariant multiplicities of Coxeter arrangements and invariant bases2012

    • Author(s)
      Takuro Abe, Hiroaki Terao, Atsushi Wakamiko
    • Journal Title

      Advances in Math.

      Volume: 230 Pages: 2364-2377

    • Peer Reviewed
  • [Journal Article] The Shi arrangement of the type $D_\ell$2012

    • Author(s)
      Ruimei Gao, Donghe Pei, Hiroaki Terao
    • Journal Title

      Proc. Japan Acad. Ser. A Math. Sci.

      Volume: 88 Pages: 41-45

    • Peer Reviewed
  • [Journal Article] The freeness of Shi-Catalan arrangements2011

    • Author(s)
      Takuro Abe, Hiroaki Terao
    • Journal Title

      European J. Combin.

      Volume: 32 Pages: 1191-1198

    • Peer Reviewed
  • [Journal Article] Ranking patterns of unfolding models of codimension one2011

    • Author(s)
      Hidehiko Kamiya, Akimichi Takemura, Hiroaki Terao
    • Journal Title

      Advances in Applied Mathematics

      Volume: 47 Pages: 379-400

    • Peer Reviewed
  • [Journal Article] Primitive filtrations of the modules of invariant logarithmic forms of Coxeter arrangements2011

    • Author(s)
      Takuro Abe, Hiroaki Terao
    • Journal Title

      Journal of Algebra

      Volume: 330 Pages: 251-262

    • Peer Reviewed
  • [Journal Article] Periodicity of non-central integral arrangements modulo positive integers2011

    • Author(s)
      Hidehiko Kamiya, Akimichi Takemura, Hiroaki Terao
    • Journal Title

      Annals of Combinatorics

      Volume: 15 Pages: 449-464

    • Peer Reviewed
  • [Journal Article] A primitive derivation and logarithmic differential forms of Coxeter arrangements2010

    • Author(s)
      Takuro Abe, Hiroaki Terao
    • Journal Title

      Math. Z.

      Volume: 264 Pages: 813-828

    • Peer Reviewed
  • [Journal Article] Totally free arrangements of hyperplanes2009

    • Author(s)
      Takuro Abe, Hiroaki Terao, Masahiko Yoshinaga
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 137 Pages: 1405-1410

    • Peer Reviewed
  • [Journal Article] The Shi arrangements and the Bernoulli polynomials

    • Author(s)
      Daisuke Suyama, Hiroaki Terao
    • Journal Title

      Bull. London Math. Soc.

      Volume: (掲載確定)

    • Peer Reviewed
  • [Presentation] Primitive derivations, Shi arrangements and Bernoulli polynomials2012

    • Author(s)
      陶山大輔,寺尾宏明
    • Organizer
      the Special Session on"Singularities, Stratifications and their Applications" at an AMS Sectional Meeting
    • Place of Presentation
      University of Hawaii at Manoa(USA)
    • Year and Date
      2012-03-03
  • [Presentation] Simple bases for the logarithmic derivation modules of the generalized Shi arrangements (招待講演)2011

    • Author(s)
      寺尾宏明
    • Organizer
      Topics in the Theory of Weyl Groups and Root Systems(Sekiguchi 60)
    • Place of Presentation
      東京大学(東京都)
    • Year and Date
      2011-09-20
  • [Presentation] The Shi arrangements and the Bernoulli numbers (招待講演)2011

    • Author(s)
      寺尾宏明
    • Organizer
      the Special Session on The Algebraic Geometry and Topology of Hyperplane Arrangements at an AMS Sectional Meeting
    • Place of Presentation
      College of the Holy Cross(USA)
    • Year and Date
      2011-04-09
  • [Presentation] Combinatorial and algebro-geometric properties of free arrangements2010

    • Author(s)
      寺尾宏明
    • Organizer
      Workshop on Algebra and Geometry of Configuration Spaces and related structures
    • Place of Presentation
      Centro di ricerca matematica Ennio De Giorgi (Italy)
    • Year and Date
      2010-06-22
  • [Presentation] 超平面配置の数学(日本数学会代数学賞受賞特別講演)(招待講演)2010

    • Author(s)
      寺尾宏明
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶応大学(東京都)
    • Year and Date
      2010-03-26
  • [Presentation] Mathematics related to hyperplane arrangements2010

    • Author(s)
      寺尾宏明
    • Organizer
      Geometry of singularities and related topics
    • Place of Presentation
      東京理科大学(東京都)
    • Year and Date
      2010-03-13
  • [Book] Arrangements of Hyperplanes-Sapporo, 2009, (pp.570) Advanced Studies in Pure Math.2012

    • Author(s)
      Hiroaki Terao, Sergey Yuzvinsky
    • Total Pages
      62
    • Publisher
      Mathematical Society of Japan
  • [Book] The characteristic quasi-polynomials of the arrangements of root systems and mid-hyperplane arrangements, in : Progress in Math. 283, Arrangements, local systems and singularities2010

    • Author(s)
      Hidehiko Kamiya, Akimichi Takemura, Hiroaki Terao
    • Total Pages
      177-190
    • Publisher
      Birkhauser
  • [Book] Arrangements stable under the Coxeter groups, in : Configuration Spaces : Geometry, Topology and Combinatorics, Proceedings of a special period at the De Giorgi Center, Scuola Normale in Pisa

    • Author(s)
      Hidehiko Kamiya, Akimichi Takemura, Hiroaki Terao
    • Publisher
      Edizioni della Normale, Pisa
  • [Remarks]

    • URL

      http://www.math.sci.hokudai.ac.jp/~terao/

  • [Remarks] Researcher ID Hiroaki Terao RID : A-7771-2012

URL: 

Published: 2013-07-31  

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