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Nakai Isao  中居 功

ORCIDConnect your ORCID iD *help
… Alternative Names

NAKAI Isao  中居 功

中尾 功  ナカオ イワオ

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Researcher Number 90207704
External Links
Affiliation (Current) 2025: お茶の水女子大学, , 名誉教授
2025: お茶の水女子大学, 基幹研究院, 教授
Affiliation (based on the past Project Information) *help 2015 – 2018: お茶の水女子大学, 基幹研究院, 教授
2011 – 2013: お茶の水女子大学, 大学院人間文化創成科学研究科, 教授
2009 – 2010: お茶の水女子大学, 理学部, 教授
2002 – 2006: お茶の水女子大学, 理学部, 教授
1999 – 2000: お茶の水女子大学, 理学部, 教授 … More
1998: 北海道大学, 大学院理学研究科, 助教授
1995 – 1998: 北海道大学, 大学院・理学研究科, 助教授
1995: Hokkaido University, Graduate School of Sciences, Associate Professor, 大学院理学研究科, 助教授
1993 – 1995: 北海道大学, 理学部, 助教授
1994: 広島大学, 理学部, 助教授
1990 – 1992: 北海道大学, 理学部, 講師 Less
Review Section/Research Field
Principal Investigator
Geometry / Geometry / Global analysis
Except Principal Investigator
Geometry / 代数学・幾何学 / Geometry / Global analysis / Global analysis / Algebra
Keywords
Principal Investigator
葉層 / WEB / 常微分方程式 / 複素力学系 / WEB幾何学 / Web / co-tidal / difraction / Chern接続 / Quasi group … More / 複素力学 / Complex dynamics / Foliation / 接触構造 / 一階微分方程式 / CHERN接続 / 関係式 / 一階偏微分方程式 / 可積分系 / singularity / resonance / curvature / web / RESONANCE / ODE / CURVATURE / PLANAR WEB / 剛性 / 曲率 / 位相剛性 / 曲率形式 / WEB 幾何学 / ordinary differential equation / complex dynamics / web geometry / holomorphic diffeomorphism / complex foliation / フェルマー曲面 / Campbell-Hansdorff / Relation / Horomorphic diffeomorphism / Campbell-Hausdorff / ホロノミー / 複素解析同相 / 複素葉層構造 / Chern connection / Caustics / 可換力学 / 面積程存 / Qunsi Group / 可換力学系 / 正則ベクトル場 / Chern 接続 / Quasi Group / Cavstic / Higher Order ODE / First Order PDE / Non solvable Dynamics / Integrable system / Chern onnection / 留数公式 / pseudo group / ルジャンドル / 高階偏微分方程式 / 高階拳微分方程式 / 非可解群作用 / 特異点 / マグナス展開 / 国際研究者交流、フランスおよびイスラエル / 反復線積分 / 自由群 / 平面曲線 / センター問題 / 力学系 / Blaschke / Chern コネクション / Bott コネクション … More
Except Principal Investigator
接触変換 / 葉層構造 / 葉層 / 接触幾何学 / 特異葉層構造 / 複素力学系 / 可積分系 / モンジュ・アンペール方程式 / Monge-Ampere equation / 接触幾何 / ラグランジュ特異点 / ルジャンドル特異点 / similarity pseudogroup / qualitative theory / foliation / 相似変換擬群 / 定性論 / 留数 / Web / 局所同値問題 / 単純階別リー環 / 特異点集合 / Teichmuller space / Renormalization / Dynamical System / Julia set / Bifurcation / Fractal / Chaos / Complex Dynamics / タイヒミュラー空間論 / 放物型不動点 / 超越整関数 / 分岐理論 / マンデルブロート集合 / タイヒミュラー空間 / くりこみ / 力学系 / ジュリア集合 / 分岐 / フラクタル / カオス / minimal set / unique ergodicity / Ruelle invariant / horocycle flow / parameter rigidity / foliated cohomology / locally free lie group actions / foliations / 一竜エルゴート性 / ルエル不変量 / 極小集合 / 一意エルゴード性 / Ruelle不変量 / ホロサイクル流 / パラメータ剛性 / 葉層コホモロジー / 局所自由リー群作用 / symplectic geometry / complex dynamical system / Conley index / zeta function / variational method / integrable system / Hamiltonian system / コンレイ指数 / 力学系ゼータ関数 / シンプレクティック幾何学 / 変分法 / コシレイ指数 / ゼータ関数 / ハミルトン力学系 / Gauss-Schwarz theory / Geodesic flows and Integrade systems / Harmonic mappings and Integrable systems / Systems of higher order partial differential equations of finite type / Monge-Ampere equations / Contact transformations / 過剰決定系 / 射影部分多様体論 / 高階有限型微分方程式 / 調和写像 / 解の特異点 / Gaup.Schwary理論 / Gauss-Schwarz理論 / 測地流と可積分系 / 調和写像と可積分系 / 高階有限型微分方程式系 / exceptional minimal set / Sacksteder's Theorem / 区分線形同相群 / ブラシュケ接続 / ウエッブ / 指数公式 / 非ユニモデュラーリー群 / ミルナー数 / 留数理論 / 例外的極小集合 / サックスティーダーの定理 / developable submanifold / dual variety / Gauss mapping / Grassmannian geometry / contact geometry / symplectic defect / simple singularity / 射影微分幾何 / ケーレー8元体 / 等質空間 / 射影構造 / 可展超曲面 / ケーリー8元数体 / 接触構造 / 極小曲面 / 等径超曲面 / 可展面 / 非ホロノームホモトピー原理 / 非ホロノーム横断性定理 / ギベンタル予想 / 接触同値 / シンプレクティック・モデュライ / 可展部分多様体 / 双対多様体 / ガウス写像 / グラスマン幾何 / シンプレクティック欠損 / 単純特異点 / Hyperelliptic mopping class groups / Lagrange Stability / Integrable geodesic flow / Viscosity Solution / Quasi-linear First Order PDE / Hypergeometric Systems / Contact Transformation / 超幾何微分方程式系 / 同値問題 / 例外単純リー環 / 二階偏微分方程式系 / 二階の過剰決定系 / 例外形単純リー環 / 準線形一階偏微分方程式 / 超楕円写像類群 / ラフランシュ安定性 / 可積分測地流 / 超性解の分岐 / 準線形二階偏微分方程式 / 超幾何方程式系 / 接触交換 / Hilbert's 16th problem / Pseudo-line arrangement / Plane trigonometric curve / Open umbrella / Tangent developable / Lagrange singularity / Legendre singularity / フロント写像 / 特異葉層 / symplectic幾何 / Web幾何 / 空間曲線 / 特異点論 / 射影幾何 / ヒルベルト化問題 / ヒルベルト16問題 / 擬直線配置 / 平面三角曲線 / 笠 / モンジュアンペ-ル方程式 / 可展開面 / PL homeomorphism group / residue / foliated bundle / wob / holomerphic foliation / 同相群 / 複素葉層 / 横断的幾何構造 / PL同相群 / 葉層バンドル / 織構造 / 正則葉層 / singular varieties / characteristic classes / localization / indices and residues / singular foliations / vector fields / 正則ベクトル場 / ベットル場 / 特異多様体 / 特性類 / 局所化 / 指数と留数 / ベクトル場 / Wed / Lagrange stable / Quasi-linear differential equation / Open Whitney umbrella / Residue of a vector field / Foliation / Compactifications of C^3 / A cubic threefold / ファノ多様体 / 3次超曲面 / 複素多様体 / Lagrange安定 / Whiteneyの開いた傘 / 準線形微分方程式 / ベクトル場の留数 / C^3のcompact化 / 3次元3次超曲面 / Singular set / Unfolding theory / Singular foliation / Singularity theory / Complex analytic geometry / 特性多様体 / 解複体 / 開析理論 / 時異葉層構造 / 特異点の留数 / 開折理論 / 特異点理論 / 複素解析幾何学 / 有限型微分方程式系 / 高次ジェット空間 / 包合系 / 階別単純リー環 / 微分式系 / トーリックトポロジー / シンプレクティック幾何 / 結び目 / 群 / 多様体 / トポロジー / 位相幾何 / 平均曲率の発展方程式 / ラグランジュ特異部分多様体 / 特異性 / ハミルトン-ヤコビ方程式 / 微分式系(differential system) / 特性類の留数 / Cech-de Rham cohomology / 不変部分多様体 / 複素解析的特異葉層構造 / クレロー型方程式 / 保存則 / ハミルトン-ヤコビ-ベルマン / 微分式系(difefrential system) / Lehmannの留数 / Baum-Bottの留数 / 合成写像の位相 / 完全積分可能な微分方程式 / 写像図式 / Jet空間の層化 / 可微分写像の位相 Less
  • Research Projects

    (27 results)
  • Research Products

    (14 results)
  • Co-Researchers

    (74 People)
  •  Geometry of Planar 3-websPrincipal Investigator

    • Principal Investigator
      Nakai Isao
    • Project Period (FY)
      2015 – 2018
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Ochanomizu University
  •  Relations of formal power series of one variable and coding of space curves by iterated path integralsPrincipal Investigator

    • Principal Investigator
      NAKAI Isao
    • Project Period (FY)
      2011 – 2013
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Global analysis
    • Research Institution
      Ochanomizu University
  •  Overall study of topology

    • Principal Investigator
      MASUDA Mikiya
    • Project Period (FY)
      2007 – 2009
    • Research Category
      Grant-in-Aid for Scientific Research (A)
    • Research Field
      Geometry
    • Research Institution
      Osaka City University
  •  Research on the differential sysytems and geometric structures associated with simple graded Lie algebras

    • Principal Investigator
      YAMAGUCHI Keizo
    • Project Period (FY)
      2007 – 2010
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Geometry
    • Research Institution
      Hokkaido University
  •  Research on Complex Dynamics

    • Principal Investigator
      UEDA Tetsuo, 宍倉 光広
    • Project Period (FY)
      2003 – 2006
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Global analysis
    • Research Institution
      Kyoto University
  •  Topology of Solutions of 1st order PDEs and web gPrincipal Investigator

    • Principal Investigator
      NAKAI Isao
    • Project Period (FY)
      2002 – 2005
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Geometry
    • Research Institution
      Ochanomizu University
  •  Synthetic studies of foliations and discrete group actions

    • Principal Investigator
      MATSUMOTO Shigenori
    • Project Period (FY)
      2001 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (A)
    • Research Field
      Geometry
    • Research Institution
      Nihon University
  •  Research of Systems of Partial Differential Equations from the view point of Contact Geometry

    • Principal Investigator
      YAMAGUCHI Keizo
    • Project Period (FY)
      1999 – 2002
    • Research Category
      Grant-in-Aid for Scientific Research (A)
    • Research Field
      Geometry
    • Research Institution
      HOKKAIDO UNIVERSITY
  •  Analysis of dynamical systems and related topics in geometry

    • Principal Investigator
      ITO Hidekazu
    • Project Period (FY)
      1999 – 2000
    • Research Category
      Grant-in-Aid for Scientific Research (B).
    • Research Field
      Global analysis
    • Research Institution
      Tokyo Institute of Technology
  •  Projective contact geometry and singularity theory

    • Principal Investigator
      ISHIKAWA Goo
    • Project Period (FY)
      1998 – 2001
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Geometry
    • Research Institution
      HOKKAIDOUNIVERSITY
  •  Geometry of webs, Hamiltonian systems and complex dynamicsPrincipal Investigator

    • Principal Investigator
      NAKAI Isao
    • Project Period (FY)
      1998 – 2000
    • Research Category
      Grant-in-Aid for Scientific Research (B).
    • Research Field
      Geometry
    • Research Institution
      Ochanomizu University
      Hokkaido University
  •  Many-sided Research of Foliations

    • Principal Investigator
      NISHIMORI Toshiyuki
    • Project Period (FY)
      1998 – 2000
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      HOKKAIDO UNIVERSITY
  •  可積分系の幾何学とWeb幾何学Principal Investigator

    • Principal Investigator
      中居 功
    • Project Period (FY)
      1996
    • Research Category
      Grant-in-Aid for Scientific Research on Priority Areas
    • Research Institution
      Hokkaido University
  •  Contact Geometry of Second Order

    • Principal Investigator
      YAMAGUCHI Keizo
    • Project Period (FY)
      1996 – 1998
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Geometry
    • Research Institution
      Hokkaido Univ.
  •  First Order Partial Differential Equation and WEB GeometryPrincipal Investigator

    • Principal Investigator
      NAKAI Isao
    • Project Period (FY)
      1996 – 1997
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      HOKKAIDO UNIVERSITY
  •  Research on Complex Analytic Geometry and Singularity Theory

    • Principal Investigator
      SUWA Tatsuo
    • Project Period (FY)
      1995 – 1996
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Geometry
    • Research Institution
      Hokkaido University
  •  Foliation Theory

    • Principal Investigator
      NISHIMORI Toshiyuki
    • Project Period (FY)
      1995 – 1996
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Hokkaido University
  •  Contact geometric singularity theory of projective varieties.

    • Principal Investigator
      ISHIKAWA Go-o
    • Project Period (FY)
      1995 – 1996
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      HOKKAIDO UNIVERSITY
  •  複素解析的葉層構造の特異点の研究

    • Principal Investigator
      諏訪 立雄
    • Project Period (FY)
      1994
    • Research Category
      Grant-in-Aid for Scientific Research on Priority Areas
    • Research Institution
      Hokkaido University
  •  二階の接触幾何学

    • Principal Investigator
      山口 佳三
    • Project Period (FY)
      1994
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Hokkaido University
  •  偏微分方程式の幾何と解析

    • Principal Investigator
      泉屋 周一
    • Project Period (FY)
      1994
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Hokkaido University
  •  Study on Complex Manifolds

    • Principal Investigator
      NAKAMURA Iku
    • Project Period (FY)
      1994 – 1995
    • Research Category
      Grant-in-Aid for General Scientific Research (B)
    • Research Field
      Algebra
    • Research Institution
      Hokkaido University
  •  偏微分方程式の幾何学的理論と特異点

    • Principal Investigator
      泉屋 周一
    • Project Period (FY)
      1993
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Hokkaido University
  •  複素解析的葉層構造の特異点の研究

    • Principal Investigator
      SUWA Tatsuo
    • Project Period (FY)
      1992
    • Research Category
      Grant-in-Aid for Scientific Research on Priority Areas
    • Research Institution
      Hokkaido University
  •  二階の接触幾何学

    • Principal Investigator
      YAMAGUCHI Keizo
    • Project Period (FY)
      1992
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Hokkaido University
  •  河微分写像の位相

    • Principal Investigator
      森川 良三
    • Project Period (FY)
      1990
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Nagasaki University
  •  Research on Complex Analytic Geometry and Singularity Theory

    • Principal Investigator
      SUWA Tatsuo
    • Project Period (FY)
      1990 – 1991
    • Research Category
      Grant-in-Aid for General Scientific Research (B)
    • Research Field
      代数学・幾何学
    • Research Institution
      Hokkaido University

All 2018 2016 2015 2014 2013 2012 2011 2005

All Journal Article Presentation

  • [Journal Article] Web geometry of solutions of first order ODEs2018

    • Author(s)
      Isao Nakai
    • Journal Title

      Natural Science Report, Ochanomizu University

      Volume: 68 Pages: 1-5

    • NAID

      40021527760

    • Open Access
    • Data Source
      KAKENHI-PROJECT-15K04838
  • [Journal Article] Finding roots by a simple origami2016

    • Author(s)
      ISAO NAKAI
    • Journal Title

      Ochanomizu University Natural Science Report

      Volume: 66,no.1 Pages: 1-17

    • NAID

      120005860185

    • Peer Reviewed / Open Access
    • Data Source
      KAKENHI-PROJECT-15K04838
  • [Journal Article] Webs and Singularities2014

    • Author(s)
      NAKAI, Isao
    • Journal Title

      Journal of Singularities

      Volume: Vol 9(掲載ページ未定)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23540236
  • [Journal Article] Relations of formal diffeomorphisms2005

    • Author(s)
      Isao Nakai, Kana Yanai
    • Journal Title

      RIMS Koukyuroku 1447

      Pages: 145-163

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-14340022
  • [Journal Article] Relations of formal diffeomorphisms2005

    • Author(s)
      中居 功
    • Journal Title

      数理解析研究所講究録 1447

      Pages: 145-163

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-14340022
  • [Presentation] Web geometriy from the view point of rigidity and curvature2018

    • Author(s)
      Isao Nakai
    • Organizer
      Seminaire de Geometrie, IMB, Universite de Bordeaux I
    • Invited
    • Data Source
      KAKENHI-PROJECT-15K04838
  • [Presentation] Some topics in web geometry2015

    • Author(s)
      Isao Nakai
    • Organizer
      日本数学会秋季会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-15
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-15K04838
  • [Presentation] Relation of germs of diffeomorphisms of (C,0) and Geometry of path group2013

    • Author(s)
      Isao Nakai
    • Organizer
      Seminar on Geometry and Topology in Weizman institute
    • Place of Presentation
      Rehovot, Israel
    • Invited
    • Data Source
      KAKENHI-PROJECT-23540236
  • [Presentation] Geometry of Path group Feuilletages et equations differentielles complexes2012

    • Author(s)
      NAKAI, Isao
    • Organizer
      国際議
    • Place of Presentation
      フランス, マルセイユ CIRM 研究所
    • Year and Date
      2012-10-16
    • Data Source
      KAKENHI-PROJECT-23540236
  • [Presentation] Relation of germs of diffeomorphisms of (C,0) and Geometry of path group2012

    • Author(s)
      Isao Nakai
    • Organizer
      Feuilletages et équations différentielles complexes
    • Place of Presentation
      Luminy, France
    • Invited
    • Data Source
      KAKENHI-PROJECT-23540236
  • [Presentation] Topology of Cubic maps2011

    • Author(s)
      中居功
    • Organizer
      Journees Textiles(招待講演)
    • Place of Presentation
      Rennes, France
    • Data Source
      KAKENHI-PROJECT-23540236
  • [Presentation] Webs and Singularities Resolution of singularities and related topics2011

    • Author(s)
      NAKAI, Isao
    • Organizer
      国際会議
    • Place of Presentation
      Tordesillas, スペイン
    • Year and Date
      2011-09-22
    • Data Source
      KAKENHI-PROJECT-23540236
  • [Presentation] Topology of Cubic maps2011

    • Author(s)
      中居功
    • Organizer
      Congreso Hironaka 80(招待講演)
    • Place of Presentation
      Tordesillas, SPEIN
    • Data Source
      KAKENHI-PROJECT-23540236
  • [Presentation] Webs and Singularities Les Jornees textiles2011

    • Author(s)
      NAKAI, Isao
    • Organizer
      国際会議
    • Place of Presentation
      Universite de Rennes 1, フランス, レンヌ
    • Year and Date
      2011-11-23
    • Data Source
      KAKENHI-PROJECT-23540236
  • 1.  ISHIKAWA Goo (50176161)
    # of Collaborated Projects: 15 results
    # of Collaborated Products: 0 results
  • 2.  IZUMIYA Shuichi (80127422)
    # of Collaborated Projects: 15 results
    # of Collaborated Products: 0 results
  • 3.  YAMAGUCHI Keizo (00113639)
    # of Collaborated Projects: 12 results
    # of Collaborated Products: 0 results
  • 4.  SUWA Tatsuo (40109418)
    # of Collaborated Projects: 11 results
    # of Collaborated Products: 0 results
  • 5.  KAWAZUMI Nariya (30214646)
    # of Collaborated Projects: 4 results
    # of Collaborated Products: 0 results
  • 6.  MINAKAWA Hiroyuki (30241300)
    # of Collaborated Projects: 4 results
    # of Collaborated Products: 0 results
  • 7.  SATO Hajime (30011612)
    # of Collaborated Projects: 4 results
    # of Collaborated Products: 0 results
  • 8.  MATSUMOTO Shigenori (80060143)
    # of Collaborated Projects: 3 results
    # of Collaborated Products: 0 results
  • 9.  ONO Kaoru (20204232)
    # of Collaborated Projects: 3 results
    # of Collaborated Products: 0 results
  • 10.  NAKAMURA Iku (50022687)
    # of Collaborated Projects: 3 results
    # of Collaborated Products: 0 results
  • 11.  KIYOHARA Kazuyoshi (80153245)
    # of Collaborated Projects: 3 results
    # of Collaborated Products: 0 results
  • 12.  TOSE Nobuyuki (00183492)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 13.  田中 昇 (80025296)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 14.  TSUBOI Takashi (40114566)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 15.  MORITA Shigeyuki (70011674)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 16.  SASAKI Takeshi (00022682)
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  • 17.  NISHIMORI Toshiyuki (50004487)
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  • 56.  ITO Hidekazu (90159905)
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  • 60.  志賀 啓成 (10154189)
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  • 74.  稲生 啓行 (00362434)
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