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Geometric methods in discrete integrablesystems

Research Project

Project/Area Number 21340036
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionKobe University

Principal Investigator

YAMADA Yasuhiko  神戸大学, 大学院・理学研究科, 教授 (00202383)

Co-Investigator(Kenkyū-buntansha) NOUMI Masatohi  神戸大学, 自然科学系先端融合研究環重点研究部, 教授 (80164672)
OHTA Yasuhiro  神戸大学, 大学院・理学研究科, 教授 (10213745)
SAITO Masahiko  神戸大学, 大学院・理学研究科, 教授 (80183044)
Project Period (FY) 2009 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords離散可積分系 / ラックス表示 / 幾何学 / 特殊解 / パデ近似 / 共形場理論 / パンルヴェ方程式 / パデ補間 / 量子パンルヴェ方程式 / 特殊関数解 / 可積分系 / 楕円差分 / 超幾何函数 / 行列式表示 / q差分 / Lax形式 / AGT予想 / Fuji-Suzuki-Tsuda方程式 / ラックス形式 / 代数曲線
Research Abstract

We studied mainly the discrete Painleve equations. The Lax formalism for various cases including the elliptic difference Painleve equation of type E_8 was constructed, and its geometric characterization was clarified. We constructed the corresponding Pade interpolation problem and derive simple expressions for the Painleve equation, Lax form and special solutions. Relations among the Gauge theory, conformal field theory and quantum Painleve equations were also studied.

Report

(5 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (54 results)

All 2013 2012 2011 2010 2009 Other

All Journal Article (21 results) (of which Peer Reviewed: 21 results) Presentation (32 results) (of which Invited: 1 results) Remarks (1 results)

  • [Journal Article] Symmetries of quantum Lax equations for the Painleve equations2013

    • Author(s)
      Hajime Nagoya, Yasuhiko Yamada
    • Journal Title

      Ann. Henri Poincare

      Volume: Online First Issue: 2 Pages: 313-344

    • DOI

      10.1007/s00023-013-0237-9

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Pade interpolation for elliptic Painleve equation2013

    • Author(s)
      M.Noumi, S.Tsujimoto and Y.Yamada
    • Journal Title

      Springer Proceedings in Mathematics and Statistics

      Volume: 40 Pages: 463-482

    • DOI

      10.1007/978-1-4471-4863-0_18

    • ISBN
      9781447148623, 9781447148630
    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Pad'e interpolation for elliptic Painlev'e equation2013

    • Author(s)
      M.Noumi, S.Tsujimoto and Y.Yamada
    • Journal Title

      Springer Proceedings in Mathematics and Statistics

      Volume: 40 Pages: 463-482

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] General High-Order Rogue Waves and Their Dynamics in the Nonlinear Schrodinger Equation2012

    • Author(s)
      Y.Ohta and J.Yang
    • Journal Title

      Proc. R. Soc.

      Volume: A468 Issue: 2142 Pages: 1716-1740

    • DOI

      10.1098/rspa.2011.0640

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the tau-Functions of the Reduced Ostrovsky Equation and the A_2^(2) Two-Dimensional Toda System2012

    • Author(s)
      B.-F.Feng, K.Maruno and Y.Ohta
    • Journal Title

      J. Phys. A : Math. Theor.

      Volume: 45 Issue: 35 Pages: 355203-355203

    • DOI

      10.1088/1751-8113/45/35/355203

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] ocalization with a surface operator, Irregular conformal blocks and Open topological string2012

    • Author(s)
      H.Awata, H.Fuji, H.Kanno, M.Manabe and Y.Yamada
    • Journal Title

      Adv. Theor. Math. Phys.

      Volume: 16 Pages: 725-804

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Localization with a surface operator, Irregular conformal blocks and Open topological string2012

    • Author(s)
      H.Awata, H.Fuji, H.Kanno, M.Manabe and Y.Yamada
    • Journal Title

      Adv. Theor. Math. Phys.

      Volume: 16 Pages: 725-804

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lax formalism for q-Painleve equations with affine Weyl group symmetry of type E^(1)2011

    • Author(s)
      Y.Yamada
    • Journal Title

      nt. Math. Res. Notices

      Volume: 17 Pages: 3823-3838

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves2011

    • Author(s)
      B.-F.Feng, J.Inoguchi, K.Kajiwara, K.Maruno and Y.Ohta
    • Journal Title

      J. Phys. A : Math. Theor.

      Volume: 44 Issue: 39 Pages: 19-19

    • DOI

      10.1088/1751-8113/44/39/395201

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Discrete integrable systems and hodograph transformations arising from discrete plane curves2011

    • Author(s)
      B.-F.Feng, J.Inoguchi, K.Kajiwara, K.Maruno, Y.Ohta
    • Journal Title

      J.Phys.A : Math.Theor.

      Volume: 44 Pages: 19-19

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A quantum isomonodromy equation and its application to N=2 SU(N)gauge theories2011

    • Author(s)
      Y.Yamada
    • Journal Title

      J.Phys.A, Math.Theor.

      Volume: (Online版)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Five-dimensional AGT conjecture and the deformed Virasoro algebra2010

    • Author(s)
      H.Awata and Y.Yamada
    • Journal Title

      JHEP

      Volume: 01 Issue: 1

    • DOI

      10.1007/jhep01(2010)125

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Five-dimensional AGT relation and the deformed β-ensemble2010

    • Author(s)
      H.Awata and Y.Yamada
    • Journal Title

      Prog. Theor. Phys.

      Volume: 124 Pages: 227-262

    • NAID

      10026986583

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Five-dimensional AGT relation and the deformed β-ensemble2010

    • Author(s)
      H.Awata Y.Yamada
    • Journal Title

      Prog.Theor.Phys.

      Volume: 124 Pages: 227-262

    • NAID

      10026986583

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lax formalism for q-Painleve equations with affine Weyl group symmetry of type E^{(1)}_n2010

    • Author(s)
      Y.Yamada
    • Journal Title

      Int.Math.Res.Notices

      Volume: Online版

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Five-dimensional AGT conjecture and the deformed Virasoro algebra2010

    • Author(s)
      H.Awata, Y.Yamada
    • Journal Title

      JHEP 01

      Pages: 1-11

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized energies and integrable Dn cellular automaton2010

    • Author(s)
      A.Kuniba, R.Sakamoto, Y.Yamada
    • Journal Title

      Proceedings "Infinite Analysis 09 : New Trends in Quantum Integrable Systems"

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Lax formalism for the elliptic difference Painleve equation2009

    • Author(s)
      Y.Yamada
    • Journal Title

      SIGMA

      Volume: 5 Pages: 15-15

    • DOI

      10.3842/sigma.2009.042

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generalized energies and integrable Dncellular automaton2009

    • Author(s)
      A.Kuniba, R.Sakamoto, and Y.Yamada
    • Journal Title

      Infinite Analysis 09: New Trends in Quantum Integrable Systems

      Pages: 221-242

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Moduli spaces for linear differential equations and the Painleve equations2009

    • Author(s)
      M. van der Put and M.-H. Saito
    • Journal Title

      Ann. Inst. Fourier (Grenoble)

      Volume: 59 Pages: 2611-2667

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Lax formalism for the elliptic difference Painleve equation2009

    • Author(s)
      Y.Yamada
    • Journal Title

      SIGMA 5

      Pages: 15-15

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] Lax formalism for discrete Painleve equations2013

    • Author(s)
      Y.Yamada
    • Organizer
      8th IMACS International Conference on Nonlinear Evolution Equations (招待講演)
    • Place of Presentation
      Georgia 大学.
    • Year and Date
      2013-03-25
    • Related Report
      2012 Final Research Report
  • [Presentation] Symmetry of quantum Lax equations for the Painleve equations2012

    • Author(s)
      H.Nagoya and Y.Yamada
    • Organizer
      日本数学会無限可積分系セッション一般講演
    • Place of Presentation
      九州大学
    • Year and Date
      2012-09-18
    • Related Report
      2012 Final Research Report
  • [Presentation] An interpolation problem related with q-E^(1)_8 Painleve equation2011

    • Author(s)
      Y.Yamada
    • Organizer
      Infinit Analysis 11(招待講演)
    • Place of Presentation
      東大数理
    • Year and Date
      2011-07-28
    • Related Report
      2012 Final Research Report
  • [Presentation] An interpolation problem related with q-E^{(1)}_8 Painleve equation2011

    • Author(s)
      Y.Yamada
    • Organizer
      Infinite Analysis 11
    • Place of Presentation
      東京大学・数理科学研究科(東京都)(招待講演)
    • Year and Date
      2011-07-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] 量子 Fuji-Suzuki-Tsuda 方程式とインスタントン分配関数2011

    • Author(s)
      山田泰彦
    • Organizer
      日本数学会無限可積分系セッション一般講演
    • Place of Presentation
      早稲田大学
    • Year and Date
      2011-03-22
    • Related Report
      2012 Final Research Report
  • [Presentation] 量子Fuji-Suzuki-Tsuda方程式とインスタントン分配関数2011

    • Author(s)
      山田泰彦
    • Organizer
      日本数学会無限可積分系セッション
    • Place of Presentation
      早稲田大学(東京都)
    • Year and Date
      2011-03-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] Quantum isomonodromy deformation and N=2 gauge theory2011

    • Author(s)
      山田泰彦
    • Organizer
      物理セミナー(招待講演)
    • Place of Presentation
      静岡大理
    • Year and Date
      2011-02-04
    • Related Report
      2012 Final Research Report
  • [Presentation] Quantum isomonodromy deformation and N=2 gauge theory2011

    • Author(s)
      山田泰彦
    • Organizer
      物理セミナー
    • Place of Presentation
      静岡大学理学部(静岡県)(招待購演)
    • Year and Date
      2011-02-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] Quantum isomonodromy deformation and N=2 gauge theory2011

    • Author(s)
      山田泰彦
    • Organizer
      弦理論セミナー(招待講演)
    • Place of Presentation
      名大多元数理
    • Year and Date
      2011-01-24
    • Related Report
      2012 Final Research Report
  • [Presentation] Quantum isomonodromy deformation and N=2 gauge theory2011

    • Author(s)
      山田泰彦
    • Organizer
      弦理論セミナー
    • Place of Presentation
      名古屋大学(愛知県)(招待講演)
    • Year and Date
      2011-01-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] AGT 予想が切り開いた新たな数学の世界2010

    • Author(s)
      山田泰彦
    • Organizer
      「量子可積分系の新展開」研究会(招待講演)
    • Place of Presentation
      静岡県・富士教育研修所
    • Year and Date
      2010-12-19
    • Related Report
      2012 Final Research Report
  • [Presentation] AGT予想が切り開いた新たな数学の世界2010

    • Author(s)
      山田泰彦
    • Organizer
      「量子可積分系の新展開」研究会
    • Place of Presentation
      (静岡県)富士教育研修所(招待講演)
    • Year and Date
      2010-12-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] 共形場理論, モノドロミー保存変形と AGT 予想2010

    • Author(s)
      山田泰彦
    • Organizer
      表現論セミナー(招待講演)
    • Place of Presentation
      京大数理解析研究所
    • Year and Date
      2010-12-10
    • Related Report
      2012 Final Research Report
  • [Presentation] 共形場理論,モノドロミー保存変形とAGT予想2010

    • Author(s)
      山田泰彦
    • Organizer
      表現論セミナー
    • Place of Presentation
      京都大学数理解析研究所(京都府)(招待講演)
    • Year and Date
      2010-12-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] モノドロミー保存変形と N=2ゲージ理論2010

    • Author(s)
      山田泰彦
    • Organizer
      第4回日露ワーキングセミナー(招待講演)
    • Place of Presentation
      阪市大梅田文化交流センター.
    • Year and Date
      2010-11-30
    • Related Report
      2012 Final Research Report
  • [Presentation] モノドロミー保存変形とN=2ゲージ理論2010

    • Author(s)
      山田泰彦
    • Organizer
      第4回日露ワーキングセミナー
    • Place of Presentation
      大阪市立大学梅田文化交流センター(大阪府)(招待講演)
    • Year and Date
      2010-11-30
    • Related Report
      2010 Annual Research Report
  • [Presentation] A quantum isomonodromy equation and its application to gauge theories2010

    • Author(s)
      山田泰彦
    • Organizer
      神戸可積分系セミナー
    • Place of Presentation
      神戸大理
    • Year and Date
      2010-11-17
    • Related Report
      2012 Final Research Report
  • [Presentation] A quantum isomonodromy equation and its application to gauge theories2010

    • Author(s)
      山田泰彦
    • Organizer
      神戸可積分系セミナー
    • Place of Presentation
      神戸大学(兵庫県)
    • Year and Date
      2010-11-17
    • Related Report
      2010 Annual Research Report
  • [Presentation] N=2 ゲージ理論とモノドロミー保存変形2010

    • Author(s)
      山田泰彦
    • Organizer
      「重力・幾何・素粒子」研究会(招待講演)
    • Place of Presentation
      大阪市大理
    • Year and Date
      2010-09-29
    • Related Report
      2012 Final Research Report
  • [Presentation] N=2ゲージ理論とモノドロミー保存変形2010

    • Author(s)
      山田泰彦
    • Organizer
      「重力・幾何・素粒子」研究会
    • Place of Presentation
      大阪市立大学(大阪府)(招待講演)
    • Year and Date
      2010-09-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] E_n 型 q-Painleve 方程式の Lax 形式2010

    • Author(s)
      山田泰彦
    • Organizer
      日本数学会無限可積分系セッション一般講演
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
    • Related Report
      2012 Final Research Report
  • [Presentation] E_n型q-Painleve方程式のLax形式2010

    • Author(s)
      山田泰彦
    • Organizer
      日本数学会無限可積分系セッション
    • Place of Presentation
      名古屋大学(愛知県)
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] CFT,モノドロミー保存変形, Nekrasov 関数2010

    • Author(s)
      山田泰彦
    • Organizer
      BC 系と AGT 予想の周辺」研究会(招待講演)
    • Place of Presentation
      東大数理
    • Year and Date
      2010-09-13
    • Related Report
      2012 Final Research Report
  • [Presentation] CFT,モノドロミー保存変形,Nekrasov関数2010

    • Author(s)
      山田泰彦
    • Organizer
      「BC系とAGT予想の周辺」研究会
    • Place of Presentation
      東京大学(東京都)(招待講演)
    • Year and Date
      2010-09-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] q-Virasoro 代数とインスタントン分配関数2010

    • Author(s)
      粟田英資・山田泰彦
    • Organizer
      日本数学会無限可積分系セッション一般講演
    • Place of Presentation
      慶応大学
    • Year and Date
      2010-03-27
    • Related Report
      2012 Final Research Report
  • [Presentation] q-Virasoro 代数とインスタントン分配関数2010

    • Author(s)
      粟田英資・山田泰彦
    • Organizer
      日本数学会(無限可積分系セッション・一般講演)
    • Place of Presentation
      慶應義塾大学(東京都)
    • Year and Date
      2010-03-27
    • Related Report
      2009 Annual Research Report
  • [Presentation] 離散 Painleve 方程式の Lax 形式2009

    • Author(s)
      山田泰彦
    • Organizer
      可積分系数理とその応用
    • Place of Presentation
      はこだて未来大学
    • Year and Date
      2009-08-12
    • Related Report
      2012 Final Research Report
  • [Presentation] 離散 Painleve 方程式の Lax 形式2009

    • Author(s)
      山田泰彦
    • Organizer
      可積分系数理とその応用
    • Place of Presentation
      はこだて未来大学(北海道)
    • Year and Date
      2009-08-12
    • Related Report
      2009 Annual Research Report
  • [Presentation] Lax formalism for the elliptic difference Painleve equation2009

    • Author(s)
      Y.Yamada
    • Organizer
      Geometric aspects of discrete and ultra - discrete integrable systems
    • Place of Presentation
      Glasgow 大学
    • Year and Date
      2009-04-03
    • Related Report
      2012 Final Research Report
  • [Presentation] Lax formalism for the elliptic difference Painleve equation2009

    • Author(s)
      山田泰彦
    • Organizer
      Geometric aspects of discrete and ultra-discrete in tegrable systems
    • Place of Presentation
      Glasgow 大学(英国)
    • Year and Date
      2009-04-03
    • Related Report
      2009 Annual Research Report
  • [Presentation] Lax formalism for discrete Painlev'e equations

    • Author(s)
      Y.Yamada
    • Organizer
      8th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena
    • Place of Presentation
      Univ. Georgia
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Symmetry of quantum Lax equations for the Painlev'e equations

    • Author(s)
      H.Nagoya, Y.Yamada
    • Organizer
      日本数学会2012年度秋季総合分科会無限可積分系セッション
    • Place of Presentation
      九州大学
    • Related Report
      2012 Annual Research Report
  • [Remarks] 山田泰彦

    • URL

      http://www.math.kobe-u.ac.jp/HOME/yamaday/yamada.html

    • Related Report
      2012 Annual Research Report

URL: 

Published: 2009-04-01   Modified: 2023-03-16  

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