Study on integrable systems around the Painleve systems

• Project/Area Number: 20740089
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: The University of Tokyo
• Principal Investigator: SAKAI Hidetaka 東京大学, 大学院・数理科学研究科, 准教授 (50323465)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: パンルヴェ方程式 / 差分方程式 / 特殊函数 / 超幾何函数 / 特殊関数 / 超幾何関数 / 相空間 / 4次元 / パンルヴェ型方程式 / フック型方程式 / モノドロミー保存変形

Research Abstract

Results which are obtained in the present project are as follows :(1) A study on ordinary differential equations on rational elliptic surfaces,(2) A classification of 4-dimensional Painleve type equations associated with isomonodromic deformation theory of Fuchsian equations(4 types),(3) A classification of 4-dimensional Painleve type equations obtained from unramified linear equations(22 types)(joint work with H. Kawakami and A. Nakamura),(4) q-analog of Katz's middle convolution(joint work with M. Yamaguchi),(5) A description of Schlesinger transformation obtained by using simplectic structure(joint work with A. Dzhamay and T. Takenawa).

Research Products

• [Presentation] Degeneration scheme of 4-dimensional Painleve type equations(Joint work with H. Kawakami and A. Nakamura) (2012)
  • Author(s): 坂井秀隆
  • Organizer: Joint Mathematics Meetings, AMS Special Session
  • Place of Presentation: Hynes Convention Center, Boston, USA
  • Year and Date: 2012-01-06
• [Presentation] Degeneration scheme of 4-dimensional Painlev￥'e type equations (Joint work with H.Kawakami and A.Nakamura) (2012)
  • Author(s): 坂井秀隆
  • Organizer: Joint Mathematics Meetings, AMS Special Session
  • Place of Presentation: Hynes Convention Center, Boston, USA(招待講演)
  • Year and Date: 2012-01-06
• [Presentation] Ordinary differential equations on rational elliptic surfaces, Symmetries (2011)
  • Author(s): 坂井秀隆
  • Organizer: Integrable Systems, and Representations
  • Place of Presentation: University Lyon 1, Lyon, France
  • Year and Date: 2011-12-14
• [Presentation] Ordinary differential equations on rational elliptic Surfaces (2011)
  • Author(s): 坂井秀隆
  • Organizer: Symmetries, Integrable Systems, and Representations
  • Place of Presentation: University Lyon 1, Lyon, France(招待講演)
  • Year and Date: 2011-12-14
• [Presentation] Frontier of isomonodromic deformation theory, Infinite Analysis 11 (2011)
  • Author(s): 坂井秀隆
  • Organizer: Frontier of Integrability
  • Place of Presentation: 東京大学
  • Year and Date: 2011-07-25
• [Presentation] Frontier of isomonodromic deformation theory (2011)
  • Author(s): 坂井秀隆
  • Organizer: Infinite Analysis 11, Frontier of Integrability
  • Place of Presentation: 東京大学(招待講演)
  • Year and Date: 2011-07-25
• [Presentation] モノドロミー保存変形と4次元パンルヴェ型方程式 (2010)
  • Author(s): 坂井秀隆
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-22
• [Presentation] 4次元パンルヴェ型方程式の退化図式,可積分系数理の多様性 (2010)
  • Author(s): 坂井秀隆
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-08-19
• [Presentation] 4次元パンルヴェ型方程式の退化図式 (2010)
  • Author(s): 坂井秀隆
  • Organizer: 可積分系数理の多様性
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-08-19
• [Presentation] モノドロミー保存変形と4次元パンルヴェ型方程式,微分方程式のモノドロミーをめぐる諸問題 (2009)
  • Author(s): 坂井秀隆
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2009-02-04
• [Presentation] モノドロミー保存変形と4次元パンルヴェ型方程式 (2009)
  • Author(s): 坂井秀隆
  • Organizer: 微分方程式のモノドロミーをめぐる諸問題
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] Monodromy preserving deformation and 4-dimensional Painleve type equations (2008)
  • Author(s): 坂井秀隆
  • Organizer: From Painleve to Okamoto
  • Place of Presentation: 東京大学
  • Year and Date: 2008-06-10
• [Presentation] Monodromy preserving deformation and 4-dimensional Painleve type equations (2008)
  • Author(s): 坂井秀隆
  • Organizer: From Painleve to Okaamoto
  • Place of Presentation: 東京大学
  • Year and Date: 2008-06-10
• [Presentation] Monodromy preserving deformation and 4-dimennsional Painlv\'e type equations (2008)
  • Author(s): 坂井秀隆
  • Organizer: From Painlev \'e to Okamoto
  • Place of Presentation: 東京大学
  • Year and Date: 2008-06-10
• [Remarks]
  • URL: http://www.ms.u-tokyo.ac.jp/teacher/sakai.html
• [Remarks]
  • URL: http://researchmap.jp/sky/