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Hyperplane Arrangements and Arrow's Impossibility Theorem

Research Project

Project/Area Number 23654001
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionHokkaido University

Principal Investigator

TERAO Hiroaki  北海道大学, 理学(系)研究科(研究院), 教授 (90119058)

Research Collaborator SETTEPANELLA Simona  北海道大学, 大学院・理学研究院, 特任講師 (40721890)
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords代数的組み合わせ論 / 超平面配置 / アローの不可能性定理 / 代数的組合せ論
Research Abstract

The main purpose of this research was to apply the theory of hyperplane arrangements to social sciences. We, however, need a tremendous amount of energy to jump over a gaping divide between two different research areas. To seek for breakthroughs, we organized international seminars in the AY 2011 and AY 2012. As a result of the endeavour, a place where mathematicians and social scientists work together was created.
Explicitly speaking, S. Settepanella(Labo. of Econ. and Man., Scu. Sup. Sant'Anna (Pisa, Italy) before she moved to Hokkaido University in August, 2013) and I are at the center of the activities enabling various applications of hyperplane arrangements to the social choice theory and the decision theory.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (48 results)

All 2014 2013 2012 2011 Other

All Journal Article (11 results) (of which Peer Reviewed: 10 results) Presentation (32 results) (of which Invited: 27 results) Book (1 results) Remarks (4 results)

  • [Journal Article] The freeness of ideal subarrangements of Weyl arrangements2014

    • Author(s)
      Takuro Abe, Mohamed Barakat, Michael Cuntz, Torsten Hoge, Hiroaki Terao
    • Journal Title

      DMTCS Proceedings of FPSAC 2014 (26th International Conference on Formal Power Series and Algebraic Combinatorics)

      Volume: (印刷中)

    • URL

      http://arxiv.org/abs/1304.8033

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weyl 配置のイデアル部分配置の自由性2013

    • Author(s)
      寺尾 宏明
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1870 Pages: 115-126

    • URL

      http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1870-11.pdf

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Journal Article] Arrangements stable under the Coxeter groups. in : "Configuration Spaces : Geometry, Combinatorics and Topology"2012

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

      Edizioni Della Normale, Pisa

      Pages: 327-354

    • URL

      http://arxiv.org/abs/1103.5179

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Shi arrangements and the Bernoulli polynomials2012

    • Author(s)
      D. Suyama, H. Terao
    • Journal Title

      Bull. London Math. Soc.

      Volume: 44 Issue: 3 Pages: 563-570

    • DOI

      10.1112/blms/bdr118

    • Related Report
      2013 Final Research Report 2012 Research-status Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Equivariant multiplicities of Coxeter arrangements and invariant bases2012

    • Author(s)
      T. Abe, H. Terao, A. Wakamiko
    • Journal Title

      Advances in Mathematics

      Volume: 230 Issue: 4-6 Pages: 2364-2377

    • DOI

      10.1016/j.aim.2012.04.015

    • NAID

      120005946712

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] The Shi arrangement of the type $D_\ell$2012

    • Author(s)
      R. Gao, D. Pei, H. Terao
    • Journal Title

      Proceedings of the Japan Academy, Ser. A Mathematical Sciences

      Volume: 88 Issue: 3 Pages: 41-45

    • DOI

      10.3792/pjaa.88.41

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Arrangements stable under the Coxeter groups2012

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

      ``Configuration Spaces: Geometry, Topology and Combinatorics,'' Proceedings of a special period at the De Giorgi Center, Scuola Normale in Pisa, May - June, 2010, Edizioni Della Normale, Pisa

      Volume: なし Pages: 327-354

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Arrangements stable under the Coxeter groups.2012

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

      ``Configuration Spaces: Geometry, Topology and Combinatorics,'' Proceedings of a special period at the De Giorgi Center, Scuola Normale in Pisa, May - June, 2010, Birkhauser

      Volume: 未定

    • Related Report
      2011 Research-status Report
    • 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

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] The freeness of Shi-Catalan arrangements2011

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

      European J.Combin.

      Volume: 32 Issue: 8 Pages: 1191-1198

    • DOI

      10.1016/j.ejc.2011.06.005

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] The freeness of ideal subarrangements of Weyl arrangemens

    • Author(s)
      Takuro Abe, Mohamed Barakat, Michael Cuntz, Torsten Hoge, Hiroaki Terao
    • Journal Title

      J. Eur. Math. Soc

      Volume: (印刷中)

    • URL

      http://arxiv.org/abs/1304.8033

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Presentation] The freeness of ideal-Shi arrangements and free paths in affine Weyl arrangements (and a question)2014

    • Author(s)
      Hiroaki Terao
    • Organizer
      Workshop on "New perspectives in hyperplane and reflection arrangements"
    • Place of Presentation
      Ruhr-Universitat Bochum, Germany
    • Year and Date
      2014-02-10
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On ideal subarrangements of Weyl arrangements2013

    • Author(s)
      Hiroaki Terao
    • Organizer
      Conference on "Japanese Turkish Joint Geometry Meeting"
    • Place of Presentation
      Galatasaray University, Istanbul, Turkey
    • Year and Date
      2013-11-22
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On ideal subarrangements of Weyl arrangements2013

    • Author(s)
      Hiroaki Terao
    • Organizer
      Conference on "Hyperplane arrangements and characteristic classes"
    • Place of Presentation
      RIMS, Kyoto University, Kyoto
    • Year and Date
      2013-11-12
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Multiple addition/deletion theorems and the existence of free paths in the affine Weyl arrangements2013

    • Author(s)
      Hiroaki Terao
    • Organizer
      Combinatorics Seminar
    • Place of Presentation
      Nagoya University, Nagoya
    • Year and Date
      2013-07-11
    • Related Report
      2013 Final Research Report
  • [Presentation] The freeness of ideal subarrangements of Weyl arrangements2013

    • Author(s)
      Hiroaki Terao
    • Organizer
      Conference on "The 6th Pacific RIM Conference on Mathematics 2013"
    • Place of Presentation
      Sapporo Convention Center, Sapporo
    • Year and Date
      2013-07-02
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Logarithmic derivation modules of Shi arrangements associated with root systems2013

    • Author(s)
      Hiroaki Terao
    • Organizer
      Conference on "Hyperplane Arrangements : Combinatorial and Geometric Aspects"
    • Place of Presentation
      Ruhr-Universitat Bochum, Germany
    • Year and Date
      2013-02-21
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Finite Refection Groups, Free Arrangements, Ideal Subarrangements of Weyl arrangements2013

    • Author(s)
      Hiroaki Terao
    • Organizer
      CIMPA-UNESCO-MESR-MINECO-VIETNAM research school on "Geometry and Topology of Singular Varieties. Theory and Applications"
    • Place of Presentation
      the Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Finite Reflection Groups, Free Arrangements, Ideal Subarrangements of Weyl arrangements2013

    • Author(s)
      Hiroaki Terao
    • Organizer
      CIMPA-UNESCO-MESR-MINECO-VIETNAM research school on "Geometry and Topology of Singular Varieties. Theory and Applications
    • Place of Presentation
      the Institute of Mathematics, Vietnam Academy of Science and Technology(ヴェトナム)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Logarithmic derivation modules of Shi arrangements associated with root systems2012

    • Author(s)
      Hiroaki Terao
    • Organizer
      Workshop on "Free Divisors and Differential Equations"
    • Place of Presentation
      Tokyo University of Agriculture and Technology, Tokyo
    • Year and Date
      2012-11-08
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Logarithmic derivation modules of Shi arrangements associated with root systems2012

    • Author(s)
      Hiroaki Terao
    • Organizer
      Combinatorial Representation Theory and Related Topics
    • Place of Presentation
      RIMS, Kyoto University, Kyoto
    • Year and Date
      2012-10-11
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Primitive derivations, Shi arrangements and Bernoulli polynomials2012

    • Author(s)
      Hiroaki Terao
    • Organizer
      a colloquium talk
    • Place of Presentation
      Northeastern Normal University, Chanchun, PRC
    • Year and Date
      2012-09-28
    • Related Report
      2013 Final Research Report
  • [Presentation] Primitive derivations, Shi arrangements and Bernoulli polynomials2012

    • Author(s)
      Hiroaki Terao
    • Organizer
      2012 Shanghai Conference on Algebraic Combinatorics
    • Place of Presentation
      Shanghai Jiao Tong University, Shanghai, PRC
    • Year and Date
      2012-08-20
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Primitive derivations, Shi arrangements, Bernoulli polynomials and the height-free conjecture2012

    • Author(s)
      Hiroaki Terao
    • Organizer
      one-hour talk at the "FPSAC '12 (The 24th International Conference on Formal Power Series and Algebraic Combinatorics)"
    • Place of Presentation
      Nagoya University, Nagoya
    • Year and Date
      2012-08-02
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Height basis of Weyl arrangements2012

    • Author(s)
      Hiroaki Terao
    • Organizer
      "Arrangements in Pyrenees" School on hyperplane arrangements and related topics
    • Place of Presentation
      Universite de Pau, France
    • Year and Date
      2012-06-11
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Primitive derivations, Shi arrangements and Bernoulli polynomials2012

    • Author(s)
      Hiroaki Terao
    • Organizer
      the Special Session on "Singularities, Stratifications and their Applications" at an AMS Sectional Meeting
    • Place of Presentation
      University of Hawaii Manoa, Honolulu, HI, USA (with D. Suyama)
    • Year and Date
      2012-03-03
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Primitive derivations, Shi arrangements and Bernoulli polynomials2012

    • Author(s)
      寺尾宏明
    • Organizer
      the Special Session on "Singularities, Stratifications and their Applications" at an AMS Sectional Meeting(招待講演)
    • Place of Presentation
      University of Hawaii at Manoa(USA)
    • Related Report
      2011 Research-status Report
  • [Presentation] Simple bases for the logarithmic derivation modules of the generalized Shi arrangements2011

    • Author(s)
      Hiroaki Terao
    • Organizer
      Topics in the Theory of Weyl Groups and Root Systems (Sekiguchi 60)
    • Place of Presentation
      University of Tokyo, Tokyo
    • Year and Date
      2011-09-20
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] The Shi arrangements and the Bernoulli numbers2011

    • Author(s)
      Hiroaki Terao
    • 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, Worcester, MA, USA
    • Year and Date
      2011-04-09
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] The Shi arrangements and the Bernoulli numbers2011

    • Author(s)
      寺尾宏明
    • Organizer
      the Special Session on "The Algebraic Geometry and Topology of Hyperplane Arrangements" at an AMS Sectional Meeting(招待講演)
    • Place of Presentation
      College of the Holy Cross(USA)
    • Related Report
      2011 Research-status Report
  • [Presentation] Simple bases for the logarithmic derivation modules of the generalized Shi arrangements2011

    • Author(s)
      寺尾宏明
    • Organizer
      "Topics in the Theory of Weyl Groups and Root Systems (Sekiguchi 60)"(招待講演)
    • Place of Presentation
      東京大学(東京都)
    • Related Report
      2011 Research-status Report
  • [Presentation] The freeness of ideal subarrangements of Weyl arrangements

    • Author(s)
      Hiroaki Terao
    • Organizer
      The 6th Pacific RIM Conference on Mathematics 2013
    • Place of Presentation
      札幌コンベンションセンター(札幌市)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Multiple addition/deletion theorems and the existence of free paths in the affine Weyl arrangements

    • Author(s)
      Hiroaki Terao
    • Organizer
      Combinatorics Seminar
    • Place of Presentation
      名古屋大学(名古屋市)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On ideal subarrangements of Weyl arrangements

    • Author(s)
      Hiroaki Terao
    • Organizer
      Hyperplane arrangements and characteristic classes
    • Place of Presentation
      京都大学数理解析研究所(京都市)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On ideal subarrangements of Weyl arrangements

    • Author(s)
      Hiroaki Terao
    • Organizer
      Japanese Turkish Joint Geometry Meeting
    • Place of Presentation
      Galatasaray University(トルコ)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] The freeness of ideal-Shi arrangements and free paths in affine Weyl arrangements (and a question)

    • Author(s)
      Hiroaki Terao
    • Organizer
      New perspectives in hyperplane and reflection arrangements
    • Place of Presentation
      Ruhr-Universitat Bochum(ドイツ)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Height basis of Weyl arrangements

    • Author(s)
      Hiroaki Terao
    • Organizer
      "Arrangements in Pyrenees" School on hyperplane arrangements and related topics
    • Place of Presentation
      Universite de Pau(フランス)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Primitive derivations, Shi arrangements, Bernoulli polynomials and the height-free conjecture

    • Author(s)
      Hiroaki Terao
    • Organizer
      FPSAC '12 (The 24th International Conference on Formal Power Series and Algebraic Combinatorics)
    • Place of Presentation
      名古屋大学(名古屋市)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Primitive derivations, Shi arrangements and Bernoulli polynomials

    • Author(s)
      Hiroaki Terao
    • Organizer
      2012 Shanghai Conference on Algebraic Combinatorics
    • Place of Presentation
      Shanghai Jiao Tong University(中華人民共和国)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Primitive derivations, Shi arrangements and Bernoulli polynomials

    • Author(s)
      Hiroaki Terao
    • Organizer
      colloquium
    • Place of Presentation
      Northeastern Normal University(中華人民共和国)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Logarithmic derivation modules of Shi arrangements associated with root systems

    • Author(s)
      Hiroaki Terao
    • Organizer
      Combinatorial Representation Theory and Related Topics
    • Place of Presentation
      京都大学数理解析研究所(京都市)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Logarithmic derivation modules of Shi arrangements associated with root systems

    • Author(s)
      Hiroaki Terao
    • Organizer
      Workshop on "Free Divisors and Differential Equations"
    • Place of Presentation
      東京農工大学(小金井市)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Logarithmic derivations modules of Shi arrangements associated with root systems

    • Author(s)
      Hiroaki Terao
    • Organizer
      Conference on "Hyperplane Arrangements: Combinatorial and Geometric Aspects"
    • Place of Presentation
      Ruhr-Universitat Bochum(ドイツ)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Book] 不変量と対称性: 現代数学のこころ2013

    • Author(s)
      今井 淳・寺尾宏明・中村博昭
    • Total Pages
      292
    • Publisher
      筑摩書房
    • Related Report
      2012 Research-status Report
  • [Remarks] ホームページ

    • URL

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

    • Related Report
      2013 Final Research Report
  • [Remarks] Hiroaki Terao's Page

    • URL

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

    • Related Report
      2013 Annual Research Report
  • [Remarks] Hiroaki Terao's Page

    • URL

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

    • Related Report
      2012 Research-status Report
  • [Remarks]

    • URL

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

    • Related Report
      2011 Research-status Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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