NAKAI Isao 中居功

… Alternative Names

Researcher Number	90207704
External Links
Affiliation (Current)	2018 : お茶の水女子大学, 基幹研究院, 教授
Affiliation (based on the past Project Information) *help	2015 – 2017 : 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
Review Section/Research Field	Principal Investigator Geometry / Geometry / Global analysis Except Principal Investigator Geometry / 代数学・幾何学 / Geometry / Global analysis / Algebra / Global analysis
Keywords	Principal Investigator WEB / 常微分方程式 / 葉層 / Web / WEB幾何学 / 複素力学系 / co-tidal / Chern接続 / 可積分系 / Foliation … More Except Principal Investigator 接触変換 / 接触幾何学 / 葉層構造 / 特異葉層構造 / 葉層 / ルジャンドル特異点 / Web / モンジュ・アンペール方程式 / qualitative theory / Monge-Ampere equation / 複素力学系 / ラグランジュ特異点 / 相似変換擬群 / 可積分系 / 単純階別リー環 / foliation / similarity pseudogroup / 局所同値問題 / 接触幾何 / 特異点集合 / 定性論 / 留数 / ハミルトン-ヤコビ方程式 / マンデルブロート集合 / フラクタル / Wed / 平面三角曲線 / 準線形微分方程式 / foliated bundle / Complex analytic geometry / 準線形一階偏微分方程式 / exceptional minimal set / variational method / Legendre singularity / 可積分測地流 / 解複体 / Sacksteder's Theorem / ベットル場 / Ruelle invariant / minimal set / dual variety / 特異点の留数 / ファノ多様体 / 正則ベクトル場 / Grassmannian geometry / Foliation / 葉層コホモロジー / vector fields / Pseudo-line arrangement / 射影部分多様体論 / 双対多様体 / カオス / Fractal / 笠 / 微分式系 / Open Whitney umbrella / 解の特異点 / 織構造 / Bifurcation / 複素解析的特異葉層構造 / symplectic幾何 / PL同相群 / 複素多様体 / 接触構造 / パラメータ剛性 / 射影微分幾何 / Contact Transformation / Conley index / モンジュアンペ-ル方程式 / ヒルベルト16問題 / Residue of a vector field / 微分式系(difefrential system) / トポロジー / Renormalization / Dynamical System / characteristic classes / Integrable geodesic flow / 極小集合 / Ruelle不変量 / ウエッブ / 写像図式 / Open umbrella / ヒルベルト化問題 / Gauss-Schwarz theory / クレロー型方程式 / Julia set / 非ユニモデュラーリー群 / Geodesic flows and Integrade systems / 可微分写像の位相 / 等質空間 / 指数公式 / Lagrange安定 / 超楕円写像類群 / PL homeomorphism group / 可展超曲面 / 局所化 / 高階有限型微分方程式 / Whiteneyの開いた傘 / residue / 局所自由リー群作用 / complex dynamical system / 変分法 / Chaos / 超性解の分岐 / 例外単純リー環 / 保存則 / parameter rigidity / Plane trigonometric curve / 完全積分可能な微分方程式 / indices and residues / ルエル不変量 / 微分式系(differential system) / Quasi-linear First Order PDE / トーリックトポロジー / ミルナー数 / developable submanifold / unique ergodicity / horocycle flow / wob / 横断的幾何構造 / localization / 複素解析幾何学 / 時異葉層構造 / サックスティーダーの定理 / シンプレクティック幾何 / ケーレー8元体 / 空間曲線 / 調和写像 / Complex Dynamics / 準線形二階偏微分方程式 / 区分線形同相群 / 3次元3次超曲面 / Cech-de Rham cohomology / 接触同値 / 階別単純リー環 / Contact transformations / 同値問題 / simple singularity / 過剰決定系 / 包合系 / Tangent developable / 正則葉層 / 可展部分多様体 / 特異性 / 位相幾何 / Unfolding theory / 二階偏微分方程式系 / 合成写像の位相 / Compactifications of C^3 / Hyperelliptic mopping class groups / グラスマン幾何 / 葉層バンドル / Singular set / 例外形単純リー環 / 力学系ゼータ関数 / Gaup.Schwary理論 / Hamiltonian system / 平均曲率の発展方程式 / 接触交換 / ベクトル場 / 超幾何微分方程式系 / くりこみ / ハミルトン力学系 / 開析理論 / 可展開面 / ゼータ関数 / 同相群 / 不変部分多様体 / 高階有限型微分方程式系 / singular foliations / コシレイ指数 / A cubic threefold / singular varieties / ギベンタル予想 / symplectic geometry / タイヒミュラー空間 / 等径超曲面 / シンプレクティック欠損 / 超幾何方程式系 / 射影構造 / 一竜エルゴート性 / 分岐理論 / holomerphic foliation / 非ホロノームホモトピー原理 / 単純特異点 / 調和写像と可積分系 / 例外的極小集合 / foliated cohomology / Viscosity Solution / 複素葉層 / 擬直線配置 / 特性多様体 / 有限型微分方程式系 / integrable system / Lagrange Stability / 特性類 / contact geometry / 特異多様体 / Gauss mapping / Gauss-Schwarz理論 / ガウス写像 / 超越整関数 / Singularity theory / タイヒミュラー空間論 / 一意エルゴード性 / 指数と留数 / 多様体 / C^3のcompact化 / 開折理論 / 測地流と可積分系 / シンプレクティック幾何学 / Lagrange stable / 極小曲面 / Hypergeometric Systems / 結び目 / 群 / ブラシュケ接続 / Teichmuller space / 特異葉層 / ホロサイクル流 / ハミルトン-ヤコビ-ベルマン / フロント写像 / ケーリー8元数体 / Harmonic mappings and Integrable systems / シンプレクティック・モデュライ / ラフランシュ安定性 / Web幾何 / Singular foliation / 特性類の留数 / Quasi-linear differential equation / 分岐 / ベクトル場の留数 / 留数理論 / Monge-Ampere equations / 可展面 / 射影幾何 / zeta function / Baum-Bottの留数 / 二階の過剰決定系 / 高次ジェット空間 / Systems of higher order partial differential equations of finite type / Lehmannの留数 / 力学系 / コンレイ指数 / 特異点理論 / 特異点論 / symplectic defect / foliations / 非ホロノーム横断性定理 / Jet空間の層化 / 放物型不動点 / locally free lie group actions / 3次超曲面 / ラグランジュ特異部分多様体 / Lagrange singularity / Hilbert's 16th problem / ジュリア集合 Less

平面WEB幾何学の研究Principal InvestigatorOngoing
- Principal Investigator
  
  中居功
- 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 2016 2015 2014 2013 2012 2011 2005

All Journal Article Presentation

[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
- Open Access / Peer Reviewed
- 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] 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
- Int'l Joint Research / Invited
- 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] 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] 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 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 : 15results

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2. IZUMIYA Shuichi (80127422)

# of Collaborated Projects : 15results

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3. YAMAGUCHI Keizo (00113639)

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4. SUWA Tatsuo (40109418)

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5. KAWAZUMI Nariya (30214646)

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6. MINAKAWA Hiroyuki (30241300)

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7. SATO Hajime (30011612)

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8. MATSUMOTO Shigenori (80060143)

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9. ONO Kaoru (20204232)

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10. NAKAMURA Iku (50022687)

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38. MATSUMOTO Keiji (30229546)

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51. KIKKAWA Michihika (70032430)

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52. 須川敏幸 (30235858)

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53. TAKAMURA Masashi (60206886)

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54. MORIYAMA Youichi (80210201)

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55. 大仁田義裕 (90183764)

# of Collaborated Projects : 1results

# of Collaborated Products : 0results
56. ITO Hidekazu (90159905)

# of Collaborated Projects : 1results

# of Collaborated Products : 0results
57. TANAKA Kazunaga (20188288)

# of Collaborated Projects : 1results

# of Collaborated Products : 0results
58. KOKUBU Hiroshi (50202057)

# of Collaborated Projects : 1results

# of Collaborated Products : 0results
59. MORITA Takehiko (00192782)

# of Collaborated Projects : 1results

# of Collaborated Products : 0results
60. 志賀啓成 (10154189)

# of Collaborated Projects : 1results

# of Collaborated Products : 0results
61. INABA Takashi (40125901)

# of Collaborated Projects : 1results

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62. KANAI Masahiko (70183035)

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63. NAKAYAMA Hiromichi (30227970)

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64. ASUKE Taro (30294515)

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65. TAKEBE Takashi (60240727)

# of Collaborated Projects : 1results

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66. MAJIMA Hideyuki (50111456)

# of Collaborated Projects : 1results

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67. 伊藤敏和 (60110178)

# of Collaborated Projects : 1results

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68. 大沢健夫 (30115802)

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69. 宍倉光広 (70192606)

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70. USHIKI Shigehiro (10093197)

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# of Collaborated Products : 0results
71. TANIGUCHI Masahiko (50108974)

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72. TSUJII Masato (20251598)

# of Collaborated Projects : 1results

# of Collaborated Products : 0results
73. KISAKA Masashi (70244671)

# of Collaborated Projects : 1results

# of Collaborated Products : 0results
74. 稲生啓行 (00362434)

# of Collaborated Projects : 1results

# of Collaborated Products : 0results

NAKAI Isao 中居 功

中居 功 ナカイ イサオ

中尾 功 ナカオ イワオ

Research Projects

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平面WEB幾何学の研究Principal InvestigatorOngoing

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Relations of formal power series of one variable and coding of space curves by iterated path integralsPrincipal Investigator

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Topology of Solutions of 1st order PDEs and web gPrincipal Investigator

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Geometry of webs, Hamiltonian systems and complex dynamicsPrincipal Investigator

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可積分系の幾何学とWeb幾何学Principal Investigator

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NAKAI Isao 中居功

中居功ナカイイサオ

中尾功ナカオイワオ