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Study on integrable systems with algebra geometrical method

Research Project

Project/Area Number 19740231
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionSuzuka University of Medical Science (2008-2009)
The University of Tokyo (2007)

Principal Investigator

YAMAZAKI Rei  Suzuka University of Medical Science, 薬学部, 助教 (30431901)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,210,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords数理物理 / 可積分系 / 超離散化 / トロピカル幾何 / 代数幾何 / ヤコビ多様体 / セルオートマトン / クラスター代数 / acobi多様体 / Jacobi多様体
Research Abstract

By using algebro geometrical method, we studied the finite-dimensional discrete / ultradiscrete integrable systems. We generalized the notion of algebraically completely integrability to that of tropical geometry and piecewise-linear map, and constructed the general solution to the ultradiscrete periodic Toda lattice. We also explicitly constructed the rational solution to the Mumford system. By applying cluster algebra and cluster category, we proved the periodicity of T-system and Y-system whose origin is in quantum integrable models.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (18 results)

All 2010 2009 2008 2007 Other

All Journal Article (10 results) (of which Peer Reviewed: 9 results) Presentation (6 results) Remarks (2 results)

  • [Journal Article] Tomoki Nakanishi and Junji Suzuki, Periodicities of T-systems and Y-systems2010

    • Author(s)
      Rei Inoue, Osamu Iyama, Atsuo Kuniba
    • Journal Title

      Nagoya Mathematical Journal 197

      Pages: 59-174

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Singular fiber of the Mumford system and rational solutions to the KdV hierarchy2010

    • Author(s)
      Rei Inoue, Pol Vanhaecke, Takao Yamazaki
    • Journal Title

      Communications on Pure and Applied Mathematics 63

      Pages: 508-532

    • Related Report
      2009 Final Research Report
  • [Journal Article] Periodicities of T-systems and Y-systems2010

    • Author(s)
      Rei Inoue
    • Journal Title

      Nagoya Mathematical Journal 197

      Pages: 59-174

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Singular fiber of the Mumford system and rational solutions to the KdV hierarchy2010

    • Author(s)
      Rei Inoue
    • Journal Title

      Communications on Pure and Applied Mathematics 63

      Pages: 508-532

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A tropical analogue of Fay's trisecant identity and the ultra-discrete periodic Toda lattice2009

    • Author(s)
      Rei Inoue, Tomoyuki Takenawa
    • Journal Title

      Communications in Mathematical Physics 289

      Pages: 995-1021

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tropical Jacobian and the generic fiber of the ultra-discrete periodic Toda lattice are isomorphic2009

    • Author(s)
      Rei Inoue, Tomoyuki Takenawa
    • Journal Title

      RIMS Kokyuroku Bessatsu B 13

      Pages: 175-190

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A tropical analogue of Fay's trisecant identity and the ultra-discrete periodic Toda lattice2009

    • Author(s)
      Rei Inoue
    • Journal Title

      Communications in Mathematical Physics 289

      Pages: 995-1021

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tropical Jacobian and the generic fiber of the ultra-discrete periodic Toda lattice are isomorphic2009

    • Author(s)
      Rei Inoue
    • Journal Title

      RIMS Kokyuroku Bessatsu B13

      Pages: 175-190

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tropical spectral curves and integrable cellular automata2008

    • Author(s)
      Rei Inoue, Tomoyuki Takenawa
    • Journal Title

      International Mathematics Research Notices 2008 rnn019

      Pages: 1-27

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tropical spectral curves and integrable cellular automata2008

    • Author(s)
      Rei Inoue, Tomoyuki Takenawa
    • Journal Title

      International Mathematics Research Notices 2008

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] T and Y-systems, dilogarithm identities and cluster algebras: nonsimply laced case2010

    • Author(s)
      中西知樹
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶応義塾大学
    • Related Report
      2009 Final Research Report
  • [Presentation] T and Y-systems, dilogarithm identities and cluster algebras : nonsimply laced case2010

    • Author(s)
      中西知樹
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶應義塾大学
    • Related Report
      2009 Annual Research Report
  • [Presentation] T-systemの周期性について2009

    • Author(s)
      中西知樹
    • Organizer
      日本数学会2009年度年会
    • Place of Presentation
      東京大学
    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [Presentation] マンフォード系の退化ファイバーと有理関数解2008

    • Author(s)
      井上玲
    • Organizer
      日本数学会2008年度年会
    • Place of Presentation
      近畿大学
    • Related Report
      2009 Final Research Report 2007 Annual Research Report
  • [Presentation] Fayの恒等式のトロピカル類似と超離散周期戸田格子2008

    • Author(s)
      井上玲
    • Organizer
      日本数学会2008年度周期総合分科会
    • Place of Presentation
      東京工業大学
    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [Presentation] Tropical spectral curves and integrable cellular automata2007

    • Author(s)
      井上玲
    • Organizer
      日本数学会2007年度総合分科会
    • Place of Presentation
      東北大学
    • Related Report
      2009 Final Research Report 2007 Annual Research Report
  • [Remarks]

    • URL

      http://sites.google.com/site/reiinouesite/Home/research

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://sites.google.com/site/reiinouesite/Home/research

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

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