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The birth of modern trends on commutative algebra and convex polytopes with statistical and computational strategies

Research Project

Project/Area Number 26220701
Research Category

Grant-in-Aid for Scientific Research (S)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionOsaka University

Principal Investigator

Hibi Takayuki  大阪大学, 情報科学研究科, 教授 (80181113)

Project Period (FY) 2014-05-30 – 2019-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥179,010,000 (Direct Cost: ¥137,700,000、Indirect Cost: ¥41,310,000)
Fiscal Year 2018: ¥37,700,000 (Direct Cost: ¥29,000,000、Indirect Cost: ¥8,700,000)
Fiscal Year 2017: ¥35,880,000 (Direct Cost: ¥27,600,000、Indirect Cost: ¥8,280,000)
Fiscal Year 2016: ¥41,210,000 (Direct Cost: ¥31,700,000、Indirect Cost: ¥9,510,000)
Fiscal Year 2015: ¥45,500,000 (Direct Cost: ¥35,000,000、Indirect Cost: ¥10,500,000)
Fiscal Year 2014: ¥18,720,000 (Direct Cost: ¥14,400,000、Indirect Cost: ¥4,320,000)
Keywordsグレブナー基底 / 二項式イデアル / 凸多面体 / 実験計画 / A超幾何系 / ホロノミック勾配法 / 分割表 / 可換代数 / 単項式イデアル / 計算代数統計 / A超幾何方程式系 / トーリック環 / トーリックイデアル / 有限分配束 / マルコフ基底 / 三角形分割
Outline of Final Research Achievements

The present research project holds official events such as international conferences on commutative algebra, Groebner basis projects and workshops on convex polytopes with inviting 127 foreign researchers, including postdocs and graduate students, from overseas. It conducts the solid framework for prospective international joint research in this research field. Furthermore, cultivation of human resources of domestic and overseas young researchers is promoted. From the viewpoint of research, a huge amount of original results on the topics, including reflexive polytopes, experimental design and convex polytopes, contingency tables and polyomino ideals, A-hypergeometric systems and convex polytopes, holonomic gradient methods, binomial ideals and syzygy theory, have been obtained. It turns out that our project succeeded in inviting new trends of commutative algebra and convex polytopes.

Academic Significance and Societal Importance of the Research Achievements

可換代数も凸多面体論も、伝統的な純粋数学の研究分野である。両者の相互関係は、1980年以降、著しい発展を遂げ、可換代数と組合せ論と呼ばれる境界分野が誕生した。本基盤研究(S)は、「統計」、及び、「計算」の観点から、可換代数、及び、凸多面体論の現代的な潮流を誘うことを目的とし、その研究を展開した。その結果、可換代数と統計と凸多面体論の華麗なる三重奏を誕生させることに成功し、今後の10年間の、可換代数と凸多面体論の輝かしい展望を切り開いた。

Assessment Rating
Verification Result (Rating)

A

Result (Rating)

A: Progress in the research is steadily towards the initial goal. Expected research results are expected.

Report

(10 results)
  • 2020 Research Progress Assessment (Verification Result) ( PDF )
  • 2019 Final Research Report ( PDF )
  • 2018 Annual Research Report
  • 2017 Annual Research Report   Abstract(Research Progress Assessment) ( PDF )   Research Progress Assessment (Result) ( PDF )
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Abstract ( PDF )   Annual Research Report

Research Products

(54 results)

All 2019 2018 2017 2016 2015 2014 Other

All Int'l Joint Research (8 results) Journal Article (21 results) (of which Int'l Joint Research: 7 results,  Peer Reviewed: 21 results,  Open Access: 4 results,  Acknowledgement Compliant: 1 results) Presentation (13 results) (of which Int'l Joint Research: 8 results,  Invited: 13 results) Book (1 results) Remarks (4 results) Funded Workshop (7 results)

  • [Int'l Joint Research] Gebze Technical University(トルコ)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] McMaster University(カナダ)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Tulane University(米国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Universities Duisburg-Essen(ドイツ)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Universitaet Duisburg--Essen(ドイツ)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Universitaet Duisburg--Essen(ドイツ)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Universitaet Duisburg--Essen(ドイツ)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] Universitaet Duisburg--Essen(ドイツ)

    • Related Report
      2014 Annual Research Report
  • [Journal Article] The relevance of Freiman's theorem for combinatorial commutative algebra2019

    • Author(s)
      J. Herzog, T. Hibi and G. Zhu
    • Journal Title

      Math. Z.

      Volume: 219 Pages: 999-1014

    • DOI

      10.1007/s00209-018-2200-4

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Reflexive polytopes arising from partially ordered sets and perfect graphs2019

    • Author(s)
      Hibi Takayuki、Tsuchiya Akiyoshi
    • Journal Title

      J. Algebraic Combin.

      Volume: 49 Pages: 69-81

    • DOI

      10.1007/s10801-018-0817-3

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Regularity and h-polynomials of edge ideals2019

    • Author(s)
      T. Hibi, K. Matsuda and A. Van Tuyl
    • Journal Title

      Electron. J. Combin.

      Volume: 26

    • DOI

      10.37236/8247

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Extremal Betti numbers of edge ideals2019

    • Author(s)
      Takayuki Hibi, Kyouko Kimura, Kazunori Matsuda
    • Journal Title

      Arch. Math. (Basel)

      Volume: 印刷中 Pages: 149-155

    • DOI

      10.1007/s00013-019-01322-9

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A-hypergeometric distributions and Newton polytopes2018

    • Author(s)
      Takayama, N., Kuriki, S. and Takemura, A.
    • Journal Title

      Adv. in Appl. Math.

      Volume: 99 Pages: 109-133

    • DOI

      10.1016/j.aam.2018.05.001

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Markov bases for two-way change-point models of ladder determinantal tables2017

    • Author(s)
      Satoshi Aoki and Takayuki Hibi
    • Journal Title

      J. Algebr. Stat.

      Volume: 8

    • DOI

      10.18409/jas.v8i1.55

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Quadratic Grobner bases arising from partially ordered sets2017

    • Author(s)
      Hibi Takayuki、Matsuda Kazunori、Tsuchiya Akiyoshi
    • Journal Title

      Math. Scand.

      Volume: 121 Pages: 19-25

    • DOI

      10.7146/math.scand.a-26246

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pfaffian Systems of A-Hypergeometric Equations I, Bases of Twisted Cohomology Groups2017

    • Author(s)
      T.Hibi, K.Nishiyama, N.Takayama
    • Journal Title

      Adv. Math.

      Volume: 306 Pages: 303-327

    • DOI

      10.1016/j.aim.2016.10.021

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Unimodular equivalence of order and chain polytopes2016

    • Author(s)
      T. Hibi and N. Li
    • Journal Title

      Math. Scand.

      Volume: 118

    • DOI

      10.7146/math.scand.a-23291

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quadratic Groebner bases of twinned order polytopes2016

    • Author(s)
      T. Hibi and K. Matsuda
    • Journal Title

      European J. Combin.

      Volume: 54

    • DOI

      10.1016/j.ejc.2015.12.014

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Markov chain Monte Carlo methods for the Box-Behnken designs and centrally symmetric configurations2016

    • Author(s)
      S. Aoki, T. Hibi and H. Ohsugi
    • Journal Title

      J. Stat. Theory Pract.

      Volume: 10 Pages: 59-72

    • DOI

      10.1080/15598608.2015.1067172

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonsimple polyominoes and prime ideals2015

    • Author(s)
      Takayuki Hibi and Ayesha Qureshi
    • Journal Title

      Illinois J. Math.

      Volume: 59 Pages: 391-398

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Centrally symmetric configurations of order polytopes2015

    • Author(s)
      T. Hibi, K. Matsuda, H. Ohsugi, K. Shibata
    • Journal Title

      J. Algebra

      Volume: 443 Pages: 469-478

    • DOI

      10.1016/j.jalgebra.2015.06.010

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Linear flags and Koszul filtrations2015

    • Author(s)
      Viviana Ene, Juergen Herzog and Takayuki Hibi
    • Journal Title

      Kyoto J. Math.

      Volume: 22 Pages: 517-530

    • DOI

      10.1215/21562261-3089028

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Linearly related polyominoes2015

    • Author(s)
      Viviana Ene, Juergen Herzog and Takayuki Hibi
    • Journal Title

      J. Algebraic Combin.

      Volume: 41 Pages: 949-968

    • DOI

      10.1007/s10801-014-0560-3

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Algebraic study on Cameron--Walker graphs2015

    • Author(s)
      Takayuki Hibi, Akihiro Higashitani, Kyouko Kimura, Augustine B. O'Keefe
    • Journal Title

      J. Algebra

      Volume: 422 Pages: 257-269

    • DOI

      10.1016/j.jalgebra.2014.07.037

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Integer decomposition property of dilated polytopes2014

    • Author(s)
      D. A. Cox, C. Haase, T. Hibi and A. Higashitani
    • Journal Title

      Electron. J. Combin.

      Volume: 21

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] The binomial edge ideal of a pair of graphs2014

    • Author(s)
      V. Ene, J. Herzog, T. Hibi and A. Qureshi
    • Journal Title

      Nagoya Math. J.

      Volume: 213 Pages: 105-125

    • DOI

      10.1017/s0027763000026192

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Many toric ideals generated by quadratic binomials possess no quadratic Groebner bases2014

    • Author(s)
      T. Hibi, K. Nishiyama, H. Ohsugi and A. Shikama
    • Journal Title

      J. of Algebra

      Volume: 408 Pages: 138-146

    • DOI

      10.1016/j.jalgebra.2013.09.039

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Edge rings satisfying Serre's condition (R_1)2014

    • Author(s)
      T. Hibi and L. Katthaen
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 142 Pages: 2537-2541

    • DOI

      10.1090/s0002-9939-2014-11973-3

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Depth of initial ideals of normal edge rings2014

    • Author(s)
      T. Hibi, A. Higashitani, K. Kimura, Kyouko and A. O'keefe
    • Journal Title

      Comm. Algebra

      Volume: 42 Pages: 2908-2922

    • DOI

      10.1080/00927872.2012.760565

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Presentation] The depth of a reflexive polytope2018

    • Author(s)
      T. Hibi
    • Organizer
      Combinatorial structures in algebra and geometry
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Binomial ideals arising from combinatorics2017

    • Author(s)
      T. Hibi
    • Organizer
      40th Autumn School in Algebraic Geometry
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 凸多面体と可換代数と統計の奏でる三重奏を聴く2017

    • Author(s)
      日比孝之
    • Organizer
      日本数学会「年会」応用数学分科会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] A Groebner basis characterization for chordal comparability graphs2016

    • Author(s)
      T. Hibi
    • Organizer
      Homological and Computational Methods in Commutative Algebra
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 凸多面体の不易流行2016

    • Author(s)
      日比孝之
    • Organizer
      日本数学会「年会」市民講演会
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] 凸多面体の不易流行2016

    • Author(s)
      日比孝之
    • Organizer
      日本数学会年会
    • Place of Presentation
      筑波大学・つくば市
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] ホロノミック勾配法に関する研究2016

    • Author(s)
      竹村彰通
    • Organizer
      日本数学会年会
    • Place of Presentation
      筑波大学・つくば市
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Gorenstein Fano polytopes and quadratic Gr\"obner bases2015

    • Author(s)
      日比孝之
    • Organizer
      Combinatorial and Experimental Methods in Commutative Algebra and Related Fields
    • Place of Presentation
      Universities Osnabrueck(ドイツ)
    • Year and Date
      2015-10-08
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Regularity of edge ideals and dominating induced matchings2015

    • Author(s)
      日比孝之
    • Organizer
      Minimal Free Resolutions, Betti Numbers and Combinatorics
    • Place of Presentation
      International Centre for Mathematical Sciences(イギリス)
    • Year and Date
      2015-06-04
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Gorenstein Fano polytopes and quadratic Groebner bases2015

    • Author(s)
      Takayuki Hibi
    • Organizer
      Combinatorial and Experimental Methods in Commutative Algebra and Related Fields
    • Place of Presentation
      Osnabrueck, Germany
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Regularity of edge ideals and dominating induced matchings2015

    • Author(s)
      Takayuki Hibi
    • Organizer
      Free Resolutions, Betti Numbers, and Combinatorics
    • Place of Presentation
      Edinburgh, UK
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] トーリックイデアルのグレブナー基底とその諸分野への応用2015

    • Author(s)
      大杉英史
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      京都産業大学・京都市
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Stanley's Influence on Monomial Ideals2014

    • Author(s)
      日比孝之
    • Organizer
      A conference in honor of Richard P. Stanley’s 70th birthday
    • Place of Presentation
      Massachusetts Institute of Technology(アメリカ合衆国)
    • Year and Date
      2014-06-25
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Book] Algebraic and Geometric Combinatorics on Lattice Polytopes2019

    • Author(s)
      T. Hibi and A. Tsuchiya (Eds.)
    • Total Pages
      465
    • Publisher
      World Scientific Pub Co Inc
    • ISBN
      9789811200472
    • Related Report
      2018 Annual Research Report
  • [Remarks] 日比孝之 - researchmap

    • URL

      https://researchmap.jp/read0167058

    • Related Report
      2018 Annual Research Report
  • [Remarks] 日比孝之 - 専攻案内

    • URL

      http://math.ist.osaka-u.ac.jp/course/course_hibitakayuki/

    • Related Report
      2018 Annual Research Report
  • [Remarks] 日比孝之|研究科紹介|大阪大学大学院情報科学研究科

    • URL

      http://www.ist.osaka-u.ac.jp/japanese/introduction/professors/pure-and-applied-mathematics/combinatorics/takayuki-hibi.html

    • Related Report
      2017 Annual Research Report 2016 Annual Research Report 2014 Annual Research Report
  • [Remarks] 日比孝之 研究科紹介 大阪大学大学院情報科学研究科

    • URL

      http://www.ist.osaka-u.ac.jp/japanese/introduction/professors/pure-and-applied-mathematics/combinatorics/takayuki-hibi.html

    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] The Prospects for Commutative Algebra2017

    • Related Report
      2017 Annual Research Report
  • [Funded Workshop] Application of Algebraic Methods to Statistics2016

    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] Algebraic Statistics and Symbolic Computation2016

    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] Computational Commutative Algebra and Convex Polytopes2016

    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] Binomial Ideals and Algebraic Statistics2016

    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] グレブナー基底の50年2015

    • Place of Presentation
      ホテル日航大阪
    • Year and Date
      2015-07-01
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] グレブナー基底の50年2015

    • Place of Presentation
      ホテル日航大阪(大阪)
    • Year and Date
      2015-07-01
    • Related Report
      2014 Annual Research Report

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Published: 2014-06-05   Modified: 2022-11-04  

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