GO-O Ishikawa 石川剛郎

Researcher Number	50176161
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Affiliation (Current)	2019 : 北海道大学, 理学研究院, 教授
Affiliation (based on the past Project Information) *help	2016 – 2019 : 北海道大学, 理学研究院, 教授 2011 – 2016 : 北海道大学, 理学(系)研究科(研究院), 教授 2015 : 北大, 大学院理学研究科, 教授 2015 : 北海道大学, 大学院理学研究院, 教授 2014 : 北海道大学, 大学院理学研究科, 教授 … More
Review Section/Research Field	Principal Investigator Geometry / Geometry / Global analysis / Basic Section 11020:Geometry-related / Global analysis Except Principal Investigator Geometry / Geometry / 代数学・幾何学 / Algebra / Algebra
Keywords	Principal Investigator ルジャンドル特異点 / 接触幾何 / 接触構造 / Monge-Ampere equation / ラグランジュ特異点 / 可展面 / グルサ分布 / 制御系 / グルサ系 / 特異ルジャンドル多様体 … More Except Principal Investigator 特異点 / モンジュ・アンペール方程式 / 可積分系 / 巾零解析 / 接触変換 / 巾零幾何 / 幾何構造 / 特異点論 / シンプレクティック構造 / 接触構造 / 旗多様体 / nilpotent analysis / Integrable system / 可積分測地流 / 正則曲線 / 特性類 / 特異多様体 / Web / ラグランジュ特異点 / Integrable geodesic flow / nilpotent geometry / ルジャンドル特異点 / ハミルトン力学 / 特異葉層構造 / Floer 理論 / 擬正則曲線 / Lagrange 部分多様体 / K3曲面 / 外在的幾何 / 幾何学 / 6次曲線 / シンプレクティック幾何学 / サブリーマン幾何 / Hamiltonian mechanics / リウヴィル多様体 / ミンコフスキー空間 / 特異点解消 / 微分方程式 / 基本群 / ツイスター理論 / ガウス写像 / 双対性 / 微分幾何学 / Liouville manifolds / 葉層 / 特性類の局所化 / 双曲空間 / ラグランジュ部分多様体 / 交叉理論 / カルタン接続 / 等径超曲面 / トーリック多様体 / 留数 / K3 surface / Chern類 / Sophus Lie / 接触幾何学 / Floerホモロジー / Geodesic flow / 非線形現象 / A-無限大構造 / supersingularity / フィルター付き多様体 / リー代数表現 / 衝撃波 / Riemannian geometry / フロアー・ホモロジー / fundamental group / 力学系 / contact structure / Cartan connection / rational double point / トム多項式 / 複素力学系 / Semiclassical approximation / 分岐被覆 / グルサー方程式 / singularity / クレロー方程式 / ミラー対称性 / 相対性理論 / plane curve / 超特異性 / 安定性 / インスタントン / symplectic 構造 / Floer homology / 変形理論 / lattices / Monge-Ampere equation / 擬球面 / symplectic structure / 重みつき微分方程式 / Symplectic geometry / 特異性 / Foliation / リー環の表現と微分方程式 / 単純階別リー環 / singular varieties / 単純特異点 / ハミルトン・ヤコビ方程式 / モンジュ・アンペール系 / 特異点集合 / 4頂点定理 / 国際研究者交流 / 半古典近似 / 離散化 / dual variety / Floer理論 / 微分方程式の幾何 / 格子 / Zoll / 超曲面 / ルジャンドル特異点論 / 局所同値問題 / 不変量 / コーン場 / 世界面 / ベクトル場の留数 / pseudo group / 力学素 / 符号 / Quasi-linear First Order PDE / ソフィス・リ- / 結び目理論 / Complex analytic geometry / 倉西構造 / code / カルタン幾何 / 解複体 / 周期的測地流 / Cohen-Macaulayfication / 特異点の留数 / Gravitation lens / 正則ベクトル場 / L2調和形式 / 射影部分多様体論 / 特異性類 / マッケイ対応 / 接触幾何 / 漸近解 / DS-diagram / 複素多様体 / ブレーン / 有理2重点 / 共形3対性 / 調和写像論 / ２次特性類 / グラフ型波面 / 超行列式 / Galocs cover / 近ケーラー多様体 / 粘性解 / ガウス・マニン接続 / 超曲面の幾何学 / Clairaut equation / algebraic surface / カオス性 / データ可視化 / Mackey反応 / 高階偏微分方程式 / 局所化 / 位相幾何学 / 量子コホモロジー論 / Whiteneyの開いた傘 / Einstein計量 / 測地線 / 有限型微分方程式系 / 非可解群作用 / toric多様体 / シンプレクテイック幾何 / 双曲平面 / 3次元トポロジー / 微分方程式系の不変量 / カスプ辺 / Singular varieties / ホロ平坦 / Thom-Porteous公式 / ヒルベルトスキーム / Lagrange Stability / 正標数 / ソフィス・リー / Gaup.Schwary理論 / 3次元3次超曲面 / 階別単純リー環 / 同値問題 / フランス:ドイツ:ブラジル / Ginzburg-Landau equations / Riemanu-Rochの定理 / 映像理論 / A-infinity algebra / Unfolding theory / Klein-Cartanプログラム / 局所化公式 / シンプレクテイック幾何学 / homogeneous hypersurface / 表現論 / Compactifications of C^3 / Seiberg-Witten equation / resolution of singularity / ハイパーケーラー多様体 / 例外形単純リー環 / Shock waves / Lefschetz不動点定理 / 接触交換 / ホロタイトはめ込み / A-infinity structure / 単有理性 / Residues / アインシュタイン計量 / 光錐 / モノポール方程式 / ラグランジュ・ルジャンドル部分多様体 / Chern onnection / ホモトピー論 / 非ガウス型積分 / 可積分幾何 / Simple singularity / Hamilton-Jacobi方程式 / Representation / 調和写像と可積分系 / マスロフの量子化条件 / Zoll計量 / 剛性定理 / 双曲的縮閉線 / 実多項式写像芽 / Open Whitney umbrella / 例外ホロノミー / 離散変形KdV方程式 / バンド交差 / カルノ・カラテオドリー計量 / シンブレクティック幾何学 / 重力レンズ / C^3のcompact化 / 開折理論 / フロアーホモロジー / 非ブライアント型 / Milnor数 / ガウス・ボンネ型定理 / 錐多様体 / 変換群 / ハミルトン-ヤコビ-ベルマン / 格子理論 / Harmonic mappings and Integrable systems / 大域的性質 / ルジャンドル測地線 / singular variety / 楕円体 / ヘルムホルツ方程式 / Todd類 / 垂足部分集合 / symplectic構造 / 代数曲面 / Transformation group / Systems of higher order partial differential equations of finite type / 同境 / Contact transformations / ギンツブルブランダウ方程式 / 非可換性 / pseudo holomorphic curve / ラグランジュはめ込み / スタビリィティ(安定性) / Legendre singularity theory / Lagrange部分多様体 / 構成的関数 / 射影モデル / 高階拳微分方程式 / 準線形微分方程式 / サブリーマン構造 / ruled surface / シンプレクティック多様体 / ホログラフィー原理 / McKay対応 / 旗多様体での外在的幾何 / vector fields / 軌道の幾何学 / 平均曲率流 / 微分式系 / 平均曲率一定曲面 / 解の特異点 / フランス:ドイツ:ベトナム:ブラジル / tt幾何 / Local Euler obstructions / ハミルトン変形 / 複素解析的特異葉層構造 / スペシャル幾何 / ラグランジ安定性 / 測地流 / Residue of a vector field / 微分式系(difefrential system) / 量子コホモロジー / ミンコフスキー時空 / 商特異点 / 超楕円写像類群 / 四元数ケーラー多様体 / 光化学反応 / isoparametric hypersurface / クレロー型方程式 / モノドロミ- / バミルトン力学 / ベルトラン曲線 / Viscosity Solution / ベックルント変換 / McKay correspondence / 焦集合 / 垂足曲線 / グラフ型大波面 / ギンツブルクランダウ方程式 / 超性解の分岐 / 保存則 / indices and residues / 概正則曲線 / Complex dynamics / localization / Monge-Ampere方程式 / ラプラス方程式 / 概複素曲線 / A_∞-代数 / representation of Lie algebra and system of PDEs / 過剰決定系 / 包合系 / リー環の表現と幾何 / 一階偏微分方程式 / 二階偏微分方程式系 / エンゲル・ルジャンドル双対 / 線形微分方程式系 / Hyperelliptic mopping class groups / コホモロジー / 半平坦部分接続 / Singular set / L2調和1形式 / similarity pseudogioup / Weak solution / モチビック不変量 / ベクトル場 / 4元数ケーラー多様性 / ザリスキ・ファンカンペンの定理 / リッチ流 / 開析理論 / 平均曲率の発展方程式 / 一階微分方程式 / Singularity / 波面 / foliation / 超幾何方程式系 / 特異点消去 / 平面6次曲線 / 平面曲線 / 微分幾何 / 外在幾何 / ダルブー可展開面 / 多重度 / 構造安定性 / 配置空間 / クレパント解消予想 / 余次元 / ラグランジェ部分空間対 / 余次元2 / ヘルムポルツ方程式 / アイコナル方程式 / 柊子 / 2次剰余符号 / Singularity theory / 特異ファイバー / 指数と留数 / 画像処理 / 代数多様体 / 特異Lefschetz束 / Lagrange stable / Hypergeometric Systems / flux conjecture / ザリスキ・ファンカンペン / サブリーマン多様体 / 弱解 / Klein-Cartan programme / モース理論 / Quasi-linear differential equation / Darboux枠 / 非ホロノーム分布 / 事象の地平線 / 特性類の局所他 / Floer theory / ホロ凸 / 交叉数 / 超幾何積分 / 3次コーン構造 / 極大曲面 / 次数つきリー代数表現 / 3次超曲面 / ラグランジュ特異部分多様体 / 双曲構造 / ハミルトン-ヤコビ方程式 / Wed / Singularities / A_∞-構造 / ベットル場 / Milnor類 / Lagrangian immersion / toric manifolds / First Order PDE / ファノ多様体 / 特異チャーン類 / quaolitative theory / 宇宙論 / hyperbolic Gauss map / 交点理論 / 線形偏微分方程式系の不変量 / WEB / スピントロニクス / 連接層 / シュレディンガー方程式 / 内在的幾何 / Gauss map / 双対性の曼荼羅 / Dynamical System / characteristic classes / 非線形偏微分方程式 / バルクエッジ対応 / 体積 / moduli / ホロ球面 / 可視化 / 等径関数 / Periodic geodesic flow / 超越格子 / 多項式写像芽 / ファセット面 / Lagrangian submanifold / トランスノーマル関数 / アーベル多様体 / CHERN接続 / 4 dimensional Kahler manifold / 微分式系(differential system) / Viscosity sokutions / コンピュータグラフィックス / Localization of characteristic classes / twistor theory / リー環の表現と微分方程式系 / 代数的スタック / 葉層構造 / 時異葉層構造 / スピン作用 / エントロピー / Milnor class / G_2軌道 / Fulton-Jphnsan類 / 共形３対性 / 重力場レンズ / 双曲的ガウス写像 / 特異点のモデュライ / Higher Order ODE / Gauss-Schwarz theory / コーエン・マコーレー化 / Stability / 平行超曲面 / 等質超曲面 / クウヴィル多様体 / Symplectiic geometry / ローレンツ微分幾何 / geometric structure / 準線形二階偏微分方程式 / 計算機支援 / localization of characteristic classes / 斜傾幾何学 / ガロア被覆 / サイバーグウィッテン方程式 / トランスレイティングソリトン / 局所Euler障害 / total curvature / 曲面 / 管状部分多様体 / Topology / 横断性定理 / トポロジカル絶縁体 / Hamiltonian diffeomorphisms / 複素葉層構造 / ネロン・セヴェリ格子 / 平均曲率-定曲面 / サブリーマン接触多様体 / ４頂点定理 / A-infinity構造 / pseudo-holomorphic curves / ミルナー・ファイバー / Cohomology / subriemannian geometry / 保存則の方程式 / 空間的部分多様体 / Lagrangian stability / オービフォルド / ラグランジュ・グラスマン双対 / 微分方程式の不変量 / tundamental group / exceptional minimal sec / 埋め込み / ガウス・ボンネの定理 / Riemann-Rochの定理 / ラグランジュ錐 / はめ込み / ルジャンドル / 画像処理,ブレーン宇宙 / Fulton-Johnson類 / instanton / Monge-Ampere equations / Hamilton系 / Seiberg-Witten不変量 / 極小ラグランジュ部分多様体 / バンド交差理論 / Floer cohomology / 反ド・シッター空間 / 超幾何方程式 / Lehmannの留数 / four vertices theorem / 超特異K3曲面 / ルジャンドル多様体 / 光的絶対全曲率 / スペクトル不変量 / Ricci soliton / 線形偏微分方程式 / 線織面 / quantum cohomology / Differential Geometry / 変曲点 / Conservation laws / Holomorphic foliations / 準線形一階偏微分方程式 / 共形型 / 留数公式 / モンジュ・アンベール方程式 / 例外的極小集合 / チャーン類 / パンルヴェ方程式 / lattice / ツイスター空間 / ザリスキペア / 可微分写像 / 可積分な運動 / 孤立特異点 / 2次特性類 / 位相不変量 / D_4型旗多様体 / 光的超曲面 / 切断の組 / 光的幾何学 / Contact Transformation / ハミルトン微分同相写像 / coherent sheaves / exceptional holonomy / 偏微分方程式 / リーマン多様体 / 反ドジッター空間 / Hamilton-Jacobi equations / Fulton-Johnson class / Intersection theory / 同変ホモロジー / Geodesic flows and Integrade systems / Lagrange安定 / ローレンツ空間形 / Non solvable Dynamics / グレブナー基底 / ローレンツ微分幾何学 / 例外単純リー環 / Fascet surfaces / The Eikonal equations / Gromov-Witten invariants / tt戸田格子 / 相似変換擬群 / 単純K3特異点 / 正則曲線と量子コホモロジー / 複素解析幾何学 / 例学ホロノミー / 超幾何微分方程式 / 特性曲線 / Cech-de Rham cohomology / 超幾何微分方程式系 / ルジャンドル観測線 / toric 多様体 / 焦点集合 / フロアー・コホモロジー / Chern classes / Yang-Mills接続 / Riemann-Roch / マッカイ対応 / Goursat equation / 同境群 / 調和写像 / Klein-Cartan Program / シンプレクティック・フィリング / ルジャンドル組み紐 / Gauss-Schwarz理論 / constant mean curvature surface / 不変部分多様体 / 高階有限型微分方程式系 / singular foliations / A cubic threefold / 変換群論 / フレアホモロジー / ガウス曲率 / Schwartz-MacPherson class / 全曲率 / ３次元トポロジー / オーストリア:ベラルーシュ:イタリア:フランス:ポーランド / 双曲幾何 / 距離空間のモジュライ / リー群 / multiplicity / 特性多様体 / simple singularity / D_4図式 / 運動量写像 / 等径・等質超曲面 / Riemann-Roch theorem / 4次元多様体 / Minkowski space / 曲線 / フロベニウス固有値 / 線形ワインガルテン曲面 / 測地流と可積分系 / 高階有限型微分方程式 / チャーン・マクファーソン自然変換 / モジュライ / ブラジル：フランス / Thom類 / Abelian variety / 微分方程式系 / 定性論 / 離散幾何学 / subriemannian manifold / ヒルベルトスキーム / ラフランシュ安定性 / Singular foliation / 特性類の留数 / コンピュータ・グラフィックス / Eillipsoid / 2階常微分方程式 / ケーラー・リウヴィル多様体 / リーマン幾何学 / Baum-Bottの留数 / 二階の過剰決定系 / 高次ジェット空間 / ラグランジュ・グラスマン射影双対 / filtered manifold / シューベルト計算 / リーマン・ロッホ / モーメント写像 / Complex dynamical systems / 擬正則写像 / 特異点理論 / 半正定値計量 / 光的曲面 / ルジャンドル双対性 / 終結式 / ツバメの尾曲面 / Schwartz-MacPherson類 / Lagrangian submanifolds / 部分多様体 / オルタレーション Less

Developments and Applications of Geometric Singularity TheoryPrincipal InvestigatorOngoing
- Principal Investigator
  
  石川剛郎
- Project Period (FY)
  2019 – 2022
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11020:Geometry-related
- Research Institution
  Hokkaido University
Application of sub-Riemannian geometry to vision modelPrincipal Investigator
- Principal Investigator
  
  Ishikawa Goo
- Project Period (FY)
  2015 – 2017
- Research Category
  
  Grant-in-Aid for Challenging Exploratory Research
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
Developments and applications of geometric singularity theoryPrincipal InvestigatorOngoing
- Principal Investigator
  
  石川剛郎
- Project Period (FY)
  2015 – 2018
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
Floer 理論の深化と symplectic 構造の研究Ongoing
- Principal Investigator
  
  小野薫
- Project Period (FY)
  2014 – 2018
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Geometry
- Research Institution
  Kyoto University
Geometric studies on singularity of non-linear phenomena
- Principal Investigator
  
  Izumiya Shyuichi
- Project Period (FY)
  2014 – 2017
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
Development of nilpotent geometry and nilpotent analysis II
- Principal Investigator
  
  MORIMOTO Tohru
- Project Period (FY)
  2011 – 2014
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Doshisha University
  Kinki University
The construction of infinite dimensional singularity theory of completely non-integrable systems and its applications to the singular motion-planning problemPrincipal Investigator
- Principal Investigator
  
  ISHIKAWA Goo
- Project Period (FY)
  2011 – 2013
- Research Category
  
  Grant-in-Aid for Challenging Exploratory Research
- Research Field
  
  Global analysis
- Research Institution
  Hokkaido University
New developments of singularity theory of mappings
- Principal Investigator
  
  SAEKI OSAMU
- Project Period (FY)
  2011 – 2015
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Geometry
- Research Institution
  Kyushu University
Development of Integrable Geometry
- Principal Investigator
  
  Miyaoka Reiko
- Project Period (FY)
  2011 – 2014
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  Tohoku University
Deepening three-manifold theory
- Principal Investigator
  
  KOJIMA Sadayoshi
- Project Period (FY)
  2010 – 2014
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Geometry
- Research Institution
  Tokyo Institute of Technology
Geometry of curves, surfaces and hypersurfaces with singularities
- Principal Investigator
  
  UMEHARA Masaaki
- Project Period (FY)
  2010 – 2014
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Geometry
- Research Institution
  Tokyo Institute of Technology
  Osaka University
A research on the geometric singularities of non-linear phenomena
- Principal Investigator
  
  IZUMIYA Shyuichi
- Project Period (FY)
  2010 – 2013
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
The synthetic study by real algebraic geometry, from sub-Riemannian geometry to tropical geometryPrincipal Investigator
- Principal Investigator
  
  GOO Ishikawa
- Project Period (FY)
  2010 – 2013
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Global analysis
- Research Institution
  Hokkaido University
Study on relations between differential equations and geometric structures by the method of twistor theory
- Principal Investigator
  
  MACHIDA YOSHINORI
- Project Period (FY)
  2010 – 2013
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Numazu College of Technology
Studies on Floer thoery, theory of holomorphic curves and symplectic structures, contact structures
- Principal Investigator
  
  ONO Kaoru
- Project Period (FY)
  2009 – 2013
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Geometry
- Research Institution
  Kyoto University
  Hokkaido University
量子フェーズ特異点論と新しい幾何光学Principal Investigator
- Principal Investigator
  
  石川剛郎
- Project Period (FY)
  2009 – 2010
- Research Category
  
  Grant-in-Aid for Challenging Exploratory Research
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
K3 surfaces and related algebraic varieties
- Principal Investigator
  
  SHIMADA Ichiro
- Project Period (FY)
  2008 – 2011
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  Hiroshima University
Correlation between differential equations, geometric structures, and twistor theory
- Principal Investigator
  
  MACHIDA Yoshinori
- Project Period (FY)
  2007 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Numazu College of Technology
Fusion of geometry and the theory of integrable systems
- Principal Investigator
  
  MIYAOKA Reiko
- Project Period (FY)
  2007 – 2010
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Geometry
- Research Institution
  Tohoku 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
Developments of nilpotent geometry and nilpotent analysis
- Principal Investigator
  
  MORIMOTO Tohru
- Project Period (FY)
  2007 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Kyoto University
  Nara Women's University
トロピカル幾何の位相代数幾何への応用Principal Investigator
- Principal Investigator
  
  石川剛郎
- Project Period (FY)
  2007 – 2008
- Research Category
  
  Grant-in-Aid for Exploratory Research
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
Differential Geometry and Partial Differential Equations as an application of Singularity theory
- Principal Investigator
  
  IZUMIYA Shyuichi
- Project Period (FY)
  2006 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
Study on Floer theory and symplectic geometry
- Principal Investigator
  
  KAORU Ono
- Project Period (FY)
  2006 – 2008
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
Explicit Study of Algebraic Varieties
- Principal Investigator
  
  SHIMADA Ichiro
- Project Period (FY)
  2006 – 2007
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Hokkaido University
Equivariant theory of Chern classes, Integrals based on Euler characteristics and related topics
- Principal Investigator
  
  OHMOTO Toru
- Project Period (FY)
  2005 – 2008
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
Developments of nilpotent geometry and nilpotent analysis, and subriemannian geometry
- Principal Investigator
  
  MORIMOTO Tohru
- Project Period (FY)
  2004 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Nara Women's University
Research on several geometry from the view point of sinuglarity theory
- Principal Investigator
  
  IZUMIYA Shyuichi
- Project Period (FY)
  2003 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
Residues on Singular Varieties
- Principal Investigator
  
  SUWA Tatsuo
- Project Period (FY)
  2003 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  Niigata University
  Hokkaido University
特異点論とその応用
- Principal Investigator
  
  泉屋周一
- Project Period (FY)
  2002
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
Todd類の源を求めて
- Principal Investigator
  
  諏訪立雄
- Project Period (FY)
  2002 – 2004
- Research Category
  
  Grant-in-Aid for Exploratory Research
- Research Field
  
  Geometry
- Research Institution
  Hokkaido University
Floor homology, singularities and deformation theory
- Principal Investigator
  
  ONO Kaoru
- Project Period (FY)
  2002 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
Applied singularity theory to exterior differential systemsPrincipal Investigator
- Principal Investigator
  
  ISHIKAWA Goo
- Project Period (FY)
  2002 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
Fundamental groups of algebraic varieties
- Principal Investigator
  
  SHIMADA Ichiro
- Project Period (FY)
  2002 – 2004
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
Differential equations and theory of submanifolds
- Principal Investigator
  
  MIYAOKA Reiko
- Project Period (FY)
  2002 – 2003
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Kyushu University
  Sophia University
Twistor correspondence between different geometric structures and application to differential equations and field theory
- Principal Investigator
  
  MACHIDA Yoshinori
- Project Period (FY)
  2002 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Numazu National College of Technology
Integrable geodesic flows and Masloy's quantization condition
- Principal Investigator
  
  KIYOHARA Kazuyoshi
- Project Period (FY)
  2001 – 2002
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
Geometries related to foliations
- Principal Investigator
  
  NISHIMORI toshiyuki
- Project Period (FY)
  2001 – 2003
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
Geometric structures and differential equations on filtered manifolds
- Principal Investigator
  
  MORIMOTO Tohru
- Project Period (FY)
  2001 – 2003
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Nara Women's University
コントロール理論への特異点論の応用Principal Investigator
- Principal Investigator
  
  石川剛郎
- Project Period (FY)
  2000 – 2001
- Research Category
  
  Grant-in-Aid for Exploratory Research
- Research Field
  
  Global analysis
- Research Institution
  Hokkaido 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
Research on Characteristic Classes of Singular Varieties
- Principal Investigator
  
  SUWA Tatsuo
- Project Period (FY)
  1999 – 2001
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
Symplectic structures and singularities
- Principal Investigator
  
  ONO Kaoru
- Project Period (FY)
  1999 – 2001
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
Integrable geodesic flows and semi-classical approximations
- Principal Investigator
  
  KIYOHARA Kazuyoshi
- Project Period (FY)
  1999 – 2000
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
Singularity theoretical research on Partial Differential Equations and Differential Geometry
- Principal Investigator
  
  IZUMIYA Shyuichi
- Project Period (FY)
  1998 – 2001
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
Projective contact geometry and singularity theoryPrincipal Investigator
- Principal Investigator
  
  ISHIKAWA Goo
- Project Period (FY)
  1998 – 2001
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDOUNIVERSITY
Geometric and group-theoretic studies on differential equations
- Principal Investigator
  
  MORIMOTO Tohru
- Project Period (FY)
  1998 – 1999
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  Nara Women's University
  Kyoto University of Education
Resolution of singularities in arbitrary characteristic
- Principal Investigator
  
  KURANO Kazuhiko
- Project Period (FY)
  1998 – 1999
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  TOKYO METOROPOLITAN UNIVERSITY
Classical theory and quantization on integrable geodesic flows
- Principal Investigator
  
  KIYOHARA Kazuyoshi
- Project Period (FY)
  1997 – 1998
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
Study of singularities and geometry by means of representation theory
- Principal Investigator
  
  NAKAMURA Iku
- Project Period (FY)
  1996 – 1999
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Geometry
- Research Institution
  HOKKAIDO UNIVERSITY
Geometry and Analysis of non-linear Partial Differentail Equations
- Principal Investigator
  
  IZUMIYA Shyuichi
- Project Period (FY)
  1996 – 1997
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Geometry
- 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 Geometry
- 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
Contact geometric singularity theory of projective varieties.Principal Investigator
- 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
シンプレクティック幾何と接触幾何の特異点論的研究Principal Investigator
- Principal Investigator
  
  石川剛郎
- Project Period (FY)
  1993
- Research Category
  
  Grant-in-Aid for Encouragement of Young Scientists (A)
- 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
  
  TATSUO Suwa
- 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
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

[Book] Singularities of Curves and Surfaces in Various Geometric Problems2015
- Author(s)
  Goo Ishikawa
- Total Pages
  94
- Publisher
  Center for Advanced Studies, Warsaw University of Technology, Warsaw
- Data Source
  KAKENHI-PROJECT-15K13431
[Book] 論理・集合・数学語2015
- Author(s)
  石川剛郎
- Total Pages
  190
- Publisher
  共立出版
- Data Source
  KAKENHI-PROJECT-15H03615
[Book] Singularities of Curves and Surfaces in Various Geometric Problems2015
- Author(s)
  Goo Ishikawa
- Total Pages
  94
- Publisher
  Center for Advanced Studies, Warsaw University of Technology, Warsaw
- Data Source
  KAKENHI-PROJECT-15H03615
[Book] 論理・集合・数学語2015
- Author(s)
  石川剛郎
- Total Pages
  190
- Publisher
  共立出版
- Data Source
  KAKENHI-PROJECT-15K13431
[Book] Singularity theory and Its Applications, Advanced Studies in Pure Mathematics2006
- Author(s)
  S. Izumiya, G. Ishikawa, H. Tokunaga, I. Shimada, T. Sano
- Publisher
  Mathematical Society of Japan
- Data Source
  KAKENHI-PROJECT-18340013
[Book] Singularity theory and Its Applications2006
- Author(s)
  S. Izumiya, G. Ishikawa, H. Tokunaga, I. Shimada and T. Sano
- Publisher
  Pure Mathematics vol. 43 Mathematical Society of Japan
- Data Source
  KAKENHI-PROJECT-18340013
[Book] Symplectic singularities of isotropic mappings, vol.652004
- Author(s)
  G.Ishikawa
- Publisher
  Banach Center
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340020
[Book] Perturbations of Caustics and Fronts, Vol.622004
- Author(s)
  G.Ishikawa
- Publisher
  Banach Center
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Leibniz complexity of Nash functions on differentiations2018
- Author(s)
  Goo Ishikawa, Tatsuya Yamashita
- Journal Title
  
  Journal of the Mathematical Society of Japan
  
  Volume : 印刷中
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K13431
[Journal Article] Singularities of frontals2018
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Advanced Studies in Pure Mathematics
  
  Volume : 印刷中
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K13431
[Journal Article] Singularities of frontals2018
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Advanced Studies in Pure Mathematics
  
  Volume : 印刷中
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15H03615
[Journal Article] Singularities of tangent surfaces to directed curves2018
- Author(s)
  Ishikawa G.、Yamashita T.
- Journal Title
  
  Topology and its Applications
  
  Volume : 234 Pages : 198-208
- DOI
  10.1016/j.topol.2017.11.018
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-26287009, KAKENHI-PROJECT-15H03615, KAKENHI-PROJECT-15K13431
[Journal Article] Leibniz complexity of Nash functions on differentiations2018
- Author(s)
  Goo Ishikawa, Tatsuya Yamashita
- Journal Title
  
  Journal of the Mathematical Society of Japan
  
  Volume : 印刷中
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15H03615
[Journal Article] Residual Algebraic Restrictions of Differential Forms2017
- Author(s)
  Goo Ishikawa, Stanislaw Janeczko
- Journal Title
  
  Methods and Applications of Analysis
  
  Volume : 24-1 Pages : 045-062
- Int'l Joint Research / Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K13431
[Journal Article] Residual Algebraic Restrictions of Differential Forms2017
- Author(s)
  Goo Ishikawa, Stanislaw Janeczko
- Journal Title
  
  Methods and Applications of Analysis
  
  Volume : 24-1 Pages : 045-062
- Int'l Joint Research / Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15H03615
[Journal Article] Singularities of tangent surfaces to space curves2017
- Author(s)
  Goo Ishikawa, Tatsuya Yamashita
- Journal Title
  
  Journal of Geoemtry
  
  Volume : 108 Pages : 301-318
- DOI
  10.1007/s00022-016-0341-3
- Open Access / Acknowledgement Compliant / Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15H03615, KAKENHI-PROJECT-15K13431, KAKENHI-PROJECT-26287009
[Journal Article] D_n-geometry and singularities of tangent surfaces2016
- Author(s)
  G. Ishikawa, Y. Machida, M. Takahashi
- Journal Title
  
  RIMS Kokyuroku Bessatsu,
  
  Volume : 未定
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K13431
[Journal Article] D_n-geometry and singularities of tangent surfaces2016
- Author(s)
  G. Ishikawa, Y. Machida, M. Takahashi
- Journal Title
  
  RIMS Kokyuroku Bessatsu
  
  Volume : 未定
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15H03615
[Journal Article] Singularities of tangent surfaces in Cartan's split G_2-geometry2016
- Author(s)
  Goo Ishikawa, Yoshinori Machida, Masatomo Takahashi
- Journal Title
  
  Asian J. Math.
  
  Volume : 20 Pages : 353-382
- DOI
  10.4310/ajm.2016.v20.n2.a6
- Open Access / Acknowledgement Compliant / Peer Reviewed
- Data Source
  KAKENHI-PROJECT-26400078, KAKENHI-PROJECT-15K13431, KAKENHI-PROJECT-15H03615, KAKENHI-PROJECT-26287009
[Journal Article] Classification problems on singularities of mappings and their applications2015
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Sugaku Exposition
  
  Volume : 28-2 Pages : 189-214
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K13431
[Journal Article] Monge-Ampere systems with Lagrangian pairs2015
- Author(s)
  Goo Ishikawa and Yoshinori Machida
- Journal Title
  
  Symmetry Integrability Geom. Methods Appli.
  
  Volume : 11
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-26287009
[Journal Article] Classification problems on singularities of mappings and their applications2015
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Sugaku Exposition
  
  Volume : 28-2 Pages : 189-214
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15H03615
[Journal Article] Monge-Ampere systems with Lagrangian pair2015
- Author(s)
  G. Ishikawa, Y. Machida
- Journal Title
  
  Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
  
  Volume : 11
- DOI
  10.3842/sigma.2015.081
- Open Access / Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K13431, KAKENHI-PROJECT-15H03615
[Journal Article] Geometry of D_4 conformal triality and singularities of tangent surfaces2015
- Author(s)
  Goo Ishikawa, Yoshinori Machida, Masatomo Takahashi
- Journal Title
  
  Journal of Singularities
  
  Volume : 12 Pages : 27-52
- DOI
  10.5427/jsing.2015.12c
- Open Access / Acknowledgement Compliant / Peer Reviewed
- Data Source
  KAKENHI-PROJECT-26400078, KAKENHI-PROJECT-15K13431, KAKENHI-PROJECT-15H03615
[Journal Article] Geometry of D_4 conformal triality and sibgularities of tangent surfaces2014
- Author(s)
  待田芳徳、石川剛郎、高橋雅朋
- Journal Title
  
  Hokkaido Univ. EPrints Server
  
  Volume : 1051 Pages : 1-25
- Data Source
  KAKENHI-PROJECT-22540109
[Journal Article] Tangent varieties and openings of map-germs2013
- Author(s)
  Goo Ishikawa (G. Ishikawa)
- Journal Title
  
  京都大学数理解析研究所講究録別冊
  
  Volume : B38 Pages : 119-137
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22244004
[Journal Article] Tangent varieties and openings of map-germs2013
- Author(s)
  Goo Ishikawa
- Journal Title
  
  RIMS Kokyuroku Bessatsu
  
  Volume : B38 Pages : 119-137
- URL
  http://www.kurims.kyoto-u.ac.jp/~kenkyubu/bessatsu-j.html
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340030
[Journal Article] Tangent varieties and openings of map-germs2013
- Author(s)
  Goo Ishikawa
- Journal Title
  
  RIMS Kokyuroku Bessatsu
  
  Volume : B38 Pages : 119-137
- URL
  http://www.kurims.kyoto-u.ac.jp/~kenkyubu/bessatsu-j.html
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23654058
[Journal Article] Tangent varieties and openings of map-germs2013
- Author(s)
  G. Ishikawa
- Journal Title
  
  数理解析研究所講究録別冊
  
  Volume : B38
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340030
[Journal Article] Generic bifurcations of framed curves in a space form and their envelopes2012
- Author(s)
  Goo Ishikawa (G. Ishikawa)
- Journal Title
  
  Topology and its Applications
  
  Volume : 159 Pages : 492-500
- Data Source
  KAKENHI-PROJECT-22244004
[Journal Article] Generic bifurcations of framed curves in a space form and their envelopes2012
- Author(s)
  G.Ishikawa
- Journal Title
  
  Topology and its Applications
  
  Volume : 159 Pages : 492-500
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340030
[Journal Article] Generic bifurcations of framed curves in a space form and their envelopes2012
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Topology and its Applications
  
  Volume : vol.159 Pages : 492-500
- URL
  http://www.sciencedirect.com/science/journal/01668641/159/2
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23654058
[Journal Article] 写像の特異性の分類問題とその応用2012
- Author(s)
  石川剛郎
- Journal Title
  
  数学
  
  Volume : 64-1 Pages : 75-96
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340030
[Journal Article] Symplectic invariants of parametric singularities2012
- Author(s)
  Goo Ihiskawa (G. Ishikawa)
- Journal Title
  
  Advances in Geometric Analysis, Advanced Lectures in Mathematics Series
  
  Volume : 21 Pages : 259-280
- Data Source
  KAKENHI-PROJECT-22244004
[Journal Article] Generic bifurcations of framed curves in a space form and their envelopes2012
- Author(s)
  G. Ishikawa
- Journal Title
  
  Topology and its Applications
  
  Volume : 159
- DOI
  10.1016/j.topol.2011.09.024
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23654058
[Journal Article] Singularities of tangent varieties to curves and surfaces2012
- Author(s)
  Goo Ishikawa (G. Ishikawa)
- Journal Title
  
  Journal of Singularities
  
  Volume : 6 Pages : 54-83
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22244004
[Journal Article] Singularities of tangent varieties to curves and surfaces2012
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Journal of singularities
  
  Volume : 6 Pages : 54-83
- DOI
  10.5427/jsing.2012.6f
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340011, KAKENHI-PROJECT-22340030, KAKENHI-PROJECT-23654058
[Journal Article] Classification problems on singularities of mappings and their applications2012
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Sugaku
  
  Volume : Volume64-1 Pages : 75-96
- URL
  http://mathsoc.jp/publication/sugaku/
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340030
[Journal Article] Singularities of tangent surfaces in Caetan's split G_2-geometry2012
- Author(s)
  待田芳徳、石川剛郎、高橋雅朋
- Journal Title
  
  Hokkaido Univ. EPrints Server
  
  Volume : 1020 Pages : 1-26
- Data Source
  KAKENHI-PROJECT-22540109
[Journal Article] Classification problems on singularities of mappings and their applications2012
- Author(s)
  Goo Ishikawa (G. Ishikawa)
- Journal Title
  
  Sugaku
  
  Volume : 64 Pages : 75-96
- Data Source
  KAKENHI-PROJECT-22244004
[Journal Article] Generic bifurcations of framed curves in a space form and their envelopes2012
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Topology and its Applications
  
  Volume : vol.159 Pages : 492-500
- URL
  http://www.sciencedirect.com/science/journal/01668641/159/2
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340030
[Journal Article] Asymmetry in singularities of tangent surfaces in contact-cone Legendre-null duality2011
- Author(s)
  待田芳徳、石川剛郎、高橋雅朋
- Journal Title
  
  J. Singularities
  
  Volume : 3 Pages : 126-143
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540109
[Journal Article] Asymmetry in singularities of tangent surfaces in contact-cone Legendrenull duality2011
- Author(s)
  待田芳徳, 石川剛郎, 高橋雅朋
- Journal Title
  
  Journal of Singularities
  
  Volume : 3 Pages : 126-143
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22540109
[Journal Article] Asymmetry in singularities of tangent surfaces in contact-cone Legendre-null duality2011
- Author(s)
  G.Ishikawa, Y.Machida, M.Takahashi
- Journal Title
  
  Journal of Singularities
  
  Volume : 3 Pages : 126-143
- DOI
  10.5427/jsing.2011.3h
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23654058, KAKENHI-PROJECT-23740041
[Journal Article] Generic bifurcations of framed curves in a space form and their envelopes2011
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Topology and its Applications
  
  Volume : (未定,To appear)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Generic bifurcations of framed curves in a space form and their envelopes2011
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Topology and its Applications
  
  Volume : 出版予定
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340030
[Journal Article] Asymmetry in singularities of tangent surfaces in contact-cone Legendre-null duality2011
- Author(s)
  G. Ishikawa, Y. Machida, M. Takahashi
- Journal Title
  
  Journal of Singularities
  
  Volume : vol.3 Pages : 126-143
- URL
  http://www.journalofsing.org/volume3/index.html
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23654058
[Journal Article] Asymmetry in singularities of tangent surfaces in contact-cone Legendre-null duality2011
- Author(s)
  G.Ishikawa, Y.Machida, M.Takahashi
- Journal Title
  
  Journal of Singularities
  
  Volume : 3 Pages : 126-143
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340030
[Journal Article] Asymmetry in singularities of tangent surfaces in contact-cone Legendre-null duality2011
- Author(s)
  G. Ishikawa, Y. Machida, M. Takahashi
- Journal Title
  
  Journal of Singularities
  
  Volume : vol.3 Pages : 126-143
- URL
  http://www.journalofsing.org/volume3/index.html
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340030
[Journal Article] Generic bifurcations of framed curves in aspace form and their envelopes2011
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Topology, its Applications
  
  Volume : (出版予定)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21654008
[Journal Article] Generic bifurcations of framed curves in a space form and their envelopes2011
- Author(s)
  G.Ishikawa
- Journal Title
  
  Topology and its Applications 99(To appear)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Singularities of flat extensions from generic surfaces with boundaries2010
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Differential Geometry and its Application (To appear)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Symplectic classification of parametric complex plane curves2010
- Author(s)
  G.Ishikawa
- Journal Title
  
  Annales Polonici Mathematici 99-3
  
  Pages : 263-284
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Symplectic classification of parametric complex plane curves2010
- Author(s)
  G.Ishikawa, S.Janeczko
- Journal Title
  
  Annales Polonici Mathematics (出版決定済)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21654008
[Journal Article] Singularities of flat extensions from generic surfaces with boundaries2010
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Differential Geometry and its Applications
  
  Volume : 28-3 Pages : 341-354
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340030
[Journal Article] Symplectic classification of parametric complex curves2010
- Author(s)
  G.Ishikawa, S.Janeczko
- Journal Title
  
  Ann. Polon. Math.
  
  Volume : 99 Pages : 263-284
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19340012
[Journal Article] Singularities of flat extensions from generic surfaces with boundaries2010
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Differential Geometry, its Applications
  
  Volume : 28-3 Pages : 341-354
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21654008
[Journal Article] Singularities of flat extensions from generic surfaces with boundaries2010
- Author(s)
  G.Ishikawa
- Journal Title
  
  Differential Geometry and its Application (出版決定済)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21654008
[Journal Article] Symplectic classification of parametric complex plane curves2010
- Author(s)
  G.Ishikawa, S.Janeczko
- Journal Title
  
  Annales Polonici Mathematici
  
  Volume : 99-3 Pages : 263-284
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21654008
[Journal Article] Singularities of flat extensions from generic surfaces with boundaries2010
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Differential Geometry and its Applications
  
  Volume : 28 Pages : 341-354
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Symplectic classification of parametric complex plane curves2010
- Author(s)
  G.Ishikawa, S.Janeczko
- Journal Title
  
  Annales Polonici Mathematici
  
  Volume : 99-3 Pages : 263-284
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340030
[Journal Article] Symplectic classification of parametric complex plane curves2010
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Annales Polonici Mathematici
  
  Volume : 99 Pages : 263-284
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Global classification of curves on the symplectic plane2008
- Author(s)
  G. Ishikawa
- Journal Title
  
  Contemporary Mathematics, Amer. Math. Soc. (To appear)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Bifurcations in symplectic space2008
- Author(s)
  G. Ishikawa, and S. Janeczko
- Journal Title
  
  Banach Center Publ vol.82
  
  Pages : 111-124
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17340013
[Journal Article] Zariski's moduli problem for plane branches and the classification of Legendre curve singularities2008
- Author(s)
  G. Ishikawa
- Journal Title
  
  Proceedings of the Australian-Japanese Workshop(Univ. Sydney, Australia 5-8 Sep. 2005).World Scientific
  
  Pages : 56-84
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17340013
[Journal Article] Generic singularities of implicit systems of first order differential equations on the plane2008
- Author(s)
  G.Ishikawa
- Journal Title
  
  Japanese Journal of Mathematics 3
  
  Pages : 93-119
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Global classification of curves on the symplectic plane, Contem-porary Mathematics2008
- Author(s)
  G. Ishikawa
- Journal Title
  
  Amer. Math. Soc 459
  
  Pages : 51-72
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540082
[Journal Article] Generic singularities of implicit systems of first order differential equations on the plane2008
- Author(s)
  A. A. Davydov, G. Ishikawa, S. Izumiya, W.-Z. Sun
- Journal Title
  
  Japanese Journal of Math. ematics vol.3-1
  
  Pages : 93-119
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17340013
[Journal Article] Bifurcations in symplectic space2008
- Author(s)
  G.Ishikawa
- Journal Title
  
  Banach Center Publ. 82
  
  Pages : 111-124
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Bifurcations in symplectic space2008
- Author(s)
  G. Ishikawa
- Journal Title
  
  Banach Center Publ. 82
  
  Pages : 111-124
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Generic singularities of implicit systems of first order differential equations on the plane2008
- Author(s)
  G. Ishikawa
- Journal Title
  
  Japanese J. Math. 3
  
  Pages : 93-119
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Global classification of curves on the symplectic plane2008
- Author(s)
  G. Ishikawa
- Journal Title
  
  Proc. IX Workshop on Real and Complex Singularities (Sao Carlos, 2006) Contemporary Mathematics, AMS (to appear)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17340013
[Journal Article] Generic singularities of implicit systems of first order differential equations on the plane2008
- Author(s)
  A. A. Davydov, G.Ishikawa, S. Izumiya, W. -Z. Sun
- Journal Title
  
  Japanese Journal of Mathematics Vol. 3
  
  Pages : 93-119
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340013
[Journal Article] Global classification ofcurves on the symplectic plane, Real andcomplex singularities2008
- Author(s)
  G. Ishikawa
- Journal Title
  
  Contemp. Math. 459
  
  Pages : 51-72
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340014
[Journal Article] Global classification of curves on the symplectic plane2008
- Author(s)
  G. Ishikawa
- Journal Title
  
  Proc. IX Workshop on Real and Complex Singuralities
  
  Pages : 51-72
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Generic singularities of implicit systems of first order differential equations on the plane2008
- Author(s)
  A. A. Davydov, G. Ishikawa, S. Izumiya, W. Z. Sun
- Journal Title
  
  Japanese Journal of Mathematics 3
  
  Pages : 93-119
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19340012
[Journal Article] Global classification of curves on the symplectic plane2008
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Contemp. Math. 459
  
  Pages : 51-72
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20340002
[Journal Article] Global classification of curves on the sympkctic plane2008
- Author(s)
  G. Ishikawa
- Journal Title
  
  Contemporary Mathematics (出版確定)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19654006
[Journal Article] Bifurcations in symplectic space2008
- Author(s)
  G. Ishikawa, S. Janeczko
- Journal Title
  
  Banach Center Publ vol. 82
  
  Pages : 111-124
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340013
[Journal Article] Global classification of clerves on the synylecfic Plalle2008
- Author(s)
  Goo ISHIKAWA
- Journal Title
  
  Contemporary Mathernatics 459
  
  Pages : 51-72
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19654006
[Journal Article] Generic singularities of implicit systems of first order differentialequations on the plane2008
- Author(s)
  A. A. Davydov, G. Ishikawa, S. Izumiya and W.-Z. Sun
- Journal Title
  
  Jpn. J. Math. 3
  
  Pages : 93-119
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340014
[Journal Article] Biflurcafions in srmpkcticspace2008
- Author(s)
  G, Ishikawa、S、Janeczko
- Journal Title
  
  Banach center Publications 82
  
  Pages : 111-124
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19654006
[Journal Article] Genenc suigularifies of implicit systams of first order differenfial eguafions on the plane2008
- Author(s)
  AA, Davyopov, G, Ishikawa, S, Izumiya, W-Z, Sum
- Journal Title
  
  Japanese Jaurnal of Mathemaitic 3
  
  Pages : 93-119
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19654006
[Journal Article] Global classification of curves on the symplectic plane, Proceedings of the IX Workshop on Real and Complex Singularities2008
- Author(s)
  G. Ishikawa
- Journal Title
  
  Sao Carlos, 2006, Contemp.Math. 459, Amer. Math. Soc.
  
  Pages : 51-72
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17340013
[Journal Article] Generic singularities of implicit systems of first order differential equations on the plane2008
- Author(s)
  A. A. Davydov, G.Ishikawa, S. Izumiya and W.-Z. Sun
- Journal Title
  
  Japanese Journal of Mathematics 3
  
  Pages : 93-119
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340013
[Journal Article] Generic singularities of implicit systems of first order differential equations on the plane2008
- Author(s)
  A.A.Davydov, G. Ishikawa, S.Izumiya, W.Z. Sun
- Journal Title
  
  Japanese Journal of Mathematics 3
  
  Pages : 93-119
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19340012
[Journal Article] Janeczko, Bifurcations in symplectic spac2008
- Author(s)
  G. Ishikawa, S. Janeczk
- Journal Title
  
  Banach Center Publ. vol.82
  
  Pages : 111-124
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540082
[Journal Article] Global Classification of Curves on the Symplectic Plane2008
- Author(s)
  G. Ishikawa
- Journal Title
  
  Contemporary Mathematics 459
  
  Pages : 51-72
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19340012
[Journal Article] Calssification of phase smgulanties for conplex scalar waves and their bfuraitions2007
- Author(s)
  J. Adachi, G. Ishikawa
- Journal Title
  
  Nonlineanity 20
  
  Pages : 1907-1925
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19654006
[Journal Article] Classification of phase singularities for complex scalar waves and their bifurcations2007
- Author(s)
  G.Ishikawa
- Journal Title
  
  Nonlinearity 20
  
  Pages : 1907-1925
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Zariski's moduli problem for plane branches and classification of Legeudro curve Smgularities2007
- Author(s)
  G. Ishikawa
- Journal Title
  
  Proceedings of Japan and Australia Rea land Complex Smgularities
  
  Pages : 56-84
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19654006
[Journal Article] Classification of phase singularities for complex scalar waves and their bifurcations2007
- Author(s)
  G. Ishikawa, J. Adachi
- Journal Title
  
  Nonlinearity 20
  
  Pages : 1907-1925
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340013
[Journal Article] Zariski's moduli problem for plane branches and the classification of Legendre curve singularities in Real and Complex Singularities2007
- Author(s)
  G. Ishikawa
- Journal Title
  
  Proceedings of the Australian-Japanese Workshop
  
  Pages : 56-84
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Classification of phase singularities for complex scalar waves and their bifurcations2007
- Author(s)
  G. Ishikawa
- Journal Title
  
  Nonlinearity 20
  
  Pages : 1907-1925
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19204006
[Journal Article] Singularities of improving affine spheres and surfaces of constant Gaussign curvature2006
- Author(s)
  G, Ishikawa
- Journal Title
  
  International Journal of Mathematics (印刷中)
  
  Pages : 2006-2006
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Singularities of improper affine spheres and surfaces of constant Gaussian curvature2006
- Author(s)
  G.Ishikawa
- Journal Title
  
  International Journal of Mathematics (To appear)
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Singularities of improper affine spheres and surfaces of constant Gaussian curvature2006
- Author(s)
  待田芳徳、石川剛郎
- Journal Title
  
  International J. Math. 17
  
  Pages : 269-293
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540105
[Journal Article] Singularities of improper affine spheres and surfaces of constant Gaussian curvature2006
- Author(s)
  待田芳徳、石川剛郎
- Journal Title
  
  International J. Math 17
  
  Pages : 269-293
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540105
[Journal Article] Singularities of improper affine spheres and surfaces of constant Gaussian curvature2006
- Author(s)
  G. Ishikawa, Y. Machida
- Journal Title
  
  International Journal of Mathematics Vol. 17-3
  
  Pages : 269-293
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340013
[Journal Article] Singularities of improper affine spheres and surfaces of constant Gaussian curvature2006
- Author(s)
  G.Ishikawa
- Journal Title
  
  Internat. Jour. Math. 17・3
  
  Pages : 269-293
- Data Source
  KAKENHI-PROJECT-17340013
[Journal Article] Singularities of improper affine spheres and surfaces of constant Gaussian curvature2006
- Author(s)
  G.Ishikawa
- Journal Title
  
  International Journal of Mathematics (印刷中)
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Singularities of improper affine spheres and surfaces of constant Gaussian curvature2006
- Author(s)
  Go-o Ishikawa
- Journal Title
  
  International J.Math. 17-3
  
  Pages : 1-25
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14540097
[Journal Article] Extra singularities of geometric solutions to Monge-Ampere equations of three variables2006
- Author(s)
  石川剛郎
- Journal Title
  
  数理解析研究所講究録 1502
  
  Pages : 41-53
- Data Source
  KAKENHI-PROJECT-18540105
[Journal Article] Extra singularities of geometric solutions to Monge-Ampere equations2006
- Author(s)
  待田芳徳、石川剛郎
- Journal Title
  
  数理研講究録 1502
  
  Pages : 41-53
- Data Source
  KAKENHI-PROJECT-18540105
[Journal Article] Singularities of improper affine spheres and surfaces of constant Gaussian curvature2006
- Author(s)
  石川剛郎
- Journal Title
  
  International J.Math. 17・3
  
  Pages : 1-25
- Data Source
  KAKENHI-PROJECT-14540097
[Journal Article] Singularities of improper offine spheres and surfaces of Constant Gaussian curvature2006
- Author(s)
  石川剛郎
- Journal Title
  
  International J. Math. 17・3
  
  Pages : 1-25
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14540097
[Journal Article] Singularities of improper affine spheres and surfaces of constant Gaussian curvature2006
- Author(s)
  Ishikawa, Goo
- Journal Title
  
  International J. of Math. 17
  
  Pages : 269-293
- Data Source
  KAKENHI-PROJECT-18340013
[Journal Article] Singularities of improper affine spheres and surfaces of constant Gaussian curvature2006
- Author(s)
  Go-O Ishikawa, et al.
- Journal Title
  
  International Journal of Mathematics 17
  
  Pages : 269-293
- Data Source
  KAKENHI-PROJECT-18340014
[Journal Article] Infinitesimal deformations and stability of singular Legendre submanifolds2005
- Author(s)
  G.Ishikawa
- Journal Title
  
  Asian Journal of Mathematics 9-1
  
  Pages : 133-166
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540065
[Journal Article] Infinitesimal determinants-and stability of singular Legendre submanifolds2005
- Author(s)
  G, Ishikawa
- Journal Title
  
  Asian Journal of Mathematics 9
  
  Pages : 133-166
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Infinitesimal deformations and stability of singular Legendre submanifolds2005
- Author(s)
  G.Ishikawa
- Journal Title
  
  Asian Journal of Mathematics 9・1
  
  Pages : 133-166
- Data Source
  KAKENHI-PROJECT-17340013
[Journal Article] Infinitesimal deformations and stability of singular Legendre submanifolds2005
- Author(s)
  Go-o Ishikawa
- Journal Title
  
  Asian Journal of Mathematics 9
  
  Pages : 133-166
- Data Source
  KAKENHI-PROJECT-14340019
[Journal Article] Infinitestimal deformations and stability of singular Legendian submanifolds2005
- Author(s)
  Goo Ishikawa
- Journal Title
  
  Asian Journal of Mathematics 9・1
  
  Pages : 133-166
- Data Source
  KAKENHI-PROJECT-15204002
[Journal Article] Infinitesimal deformations and stability of singular Legendre submanifolds2005
- Author(s)
  G.Ishikawa
- Journal Title
  
  Asian Journal of Mathematics Vol.9
  
  Pages : 133-166
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Infinitesimal deformations and stability of singular Legendre submanifolds2005
- Author(s)
  G.Ishikawa
- Journal Title
  
  Asian Journal of Mathematics 9-1
  
  Pages : 113-166
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Classifying singular Legendre canes by contact wire phisms2004
- Author(s)
  G, Ishikawa
- Journal Title
  
  Journal of Geometry and Physics 52
  
  Pages : 113-126
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Classifying singular Legendrian curves by contactmorphisms2004
- Author(s)
  G.Ishikawa
- Journal Title
  
  J.of Geometry and Physics 52
  
  Pages : 113-126
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15204002
[Journal Article] Classifying singular Legendre curves by contactomorphisms2004
- Author(s)
  G.Ishikawa
- Journal Title
  
  Journal of Geometry and Physics 52
  
  Pages : 113-126
- Data Source
  KAKENHI-PROJECT-14340019
[Journal Article] Classifying singular Legendre curves by contactomorphisms2004
- Author(s)
  G.Ishikawa
- Journal Title
  
  Journal of Geometry and Physics Vol.52--2
  
  Pages : 113-126
- Data Source
  KAKENHI-PROJECT-16540065
[Journal Article] Symplectic singularities of isofropic mappings2004
- Author(s)
  G, Ishikawa
- Journal Title
  
  Banach Center Publications 65
  
  Pages : 85-106
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Perturbations of caustics and fronts2004
- Author(s)
  G.Ishikawa
- Journal Title
  
  Barach Center Publ. 62
  
  Pages : 101-116
- Data Source
  KAKENHI-PROJECT-15340016
[Journal Article] Classifying singular Legendre curves by contactomorphisms2004
- Author(s)
  G.Ishikawa
- Journal Title
  
  J.Geom.Phys. 52
  
  Pages : 113-126
- Data Source
  KAKENHI-PROJECT-14654010
[Journal Article] Perturbations of Caustics and Front2004
- Author(s)
  G, Ishikawa
- Journal Title
  
  Banach Center Publications 62
  
  Pages : 101-116
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Symplectic singularities of isotropic mappings2004
- Author(s)
  G.Ishikawa
- Journal Title
  
  Banach Center Publication 65
  
  Pages : 85-106
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Classifying singular Legendre curves by contactmorphism2004
- Author(s)
  G.Ishikawa
- Journal Title
  
  Journal of Geometry and Physics 52
  
  Pages : 113-126
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15204002
[Journal Article] Classifying singular Legendre curves by contactomorphisms2004
- Author(s)
  G.Ishikawa
- Journal Title
  
  J.Geom.Phys. 52
  
  Pages : 113-126
- Data Source
  KAKENHI-PROJECT-15340016
[Journal Article] Classifying singular Legendre curves by contactmorphisms2004
- Author(s)
  G.Ishikawa
- Journal Title
  
  Journal of Geometry and Physics 52・2
  
  Pages : 113-126
- Data Source
  KAKENHI-PROJECT-15204002
[Journal Article] Symplectic singularities of isotropic mappings2004
- Author(s)
  G.Ishikawa, S.Janeczko
- Journal Title
  
  Banach Center Publications 65
  
  Pages : 85-106
- Data Source
  KAKENHI-PROJECT-14340019
[Journal Article] Classifying singular Legendre curves by contactomorphisms.2004
- Author(s)
  G.Ishikawa
- Journal Title
  
  Journal of Geometry and Physics. Vol.52
  
  Pages : 113-126
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Symplectic bifurcations of plane curves and isotropic liftings2003
- Author(s)
  G.Ishikawa
- Journal Title
  
  Quarterly Journal of Mathematics Vol.54
  
  Pages : 73-102
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Symplectic bifurcations of plane curves and isofropic liftings2003
- Author(s)
  G, Ishikawa
- Journal Title
  
  Quarterly Journal of Mathematics 54
  
  Pages : 73-102
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Singularities of improper affine spheres and surfaces of constant Gaussian curvature
- Author(s)
  G.Ishikawa, Y.Machida
- Journal Title
  
  International Journal of Mathematics (to appear)
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-16540065
[Journal Article] Singularities of improper affine spheres and surfaces of constant Gaussian curvature
- Author(s)
  G.Ishikawa, y.Machida
- Journal Title
  
  International Journal of Mathematics (to appear)
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540065
[Journal Article] Infinitesmal deformations and stability of singular Legendre Submanifolds
- Author(s)
  G.Ishikawa
- Journal Title
  
  Asian Journal of Mathematics (発表予定)
- Data Source
  KAKENHI-PROJECT-14340020
[Journal Article] Singularities of flat exten sions from generic surfaces with boun-daries
- Author(s)
  G. Ishikawa
- Journal Title
  
  Differential Geometry and its Application (to appear)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-19540082
[Journal Article] Duality of singular paths for (2,3,5)-distributions
- Author(s)
  G. Ishikawa, Y. Kitagawa, W. Yukuno
- Journal Title
  
  Journal of Dynamical and Control Systems
  
  Volume : (掲載確定)
- DOI
  10.1007/s10883-014-9216-9
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340030, KAKENHI-PROJECT-23654058
[Journal Article] Singularities of improper affine spheres and surfaces of constant Gaussian curvature
- Author(s)
  G.Ishikawa, Y.Machida
- Journal Title
  
  International Journal of Mathematics (to appear)
- Data Source
  KAKENHI-PROJECT-16540065
[Presentation] Duality of (2,3,5)-distributions and Lagrangian cone structures2018
- Author(s)
  Goo Ishikawa
- Organizer
  Singularities, Differential equations and Related Area
- Invited
- Data Source
  KAKENHI-PROJECT-15K13431
[Presentation] Duality of (2,3,5)-distributions and Lagrangian cone structures2018
- Author(s)
  Goo Ishikawa
- Organizer
  Contact structure, Singularities, Differential equations and related area
- Invited
- Data Source
  KAKENHI-PROJECT-15H03615
[Presentation] Duality-singularity of indefinite metrics and contact structures2017
- Author(s)
  Goo Ishikawa
- Organizer
  24th Numazu conference
- Place of Presentation
  沼津高専（静岡県・沼津市）
- Invited
- Data Source
  KAKENHI-PROJECT-15H03615
[Presentation] Duality-singularity of indefinite metrics and contact structures2017
- Author(s)
  Goo Ishikawa
- Organizer
  Contact structure, Singularities, Differential equations and related area
- Place of Presentation
  金沢大学サテライト（石川県・金沢市）
- Data Source
  KAKENHI-PROJECT-15H03615
[Presentation] Duality-singularity of indefinite metrics and contact structures2017
- Author(s)
  Goo Ishikawa
- Organizer
  Singularities in Generic Geometry and its Applications
- Int'l Joint Research / Invited
- Data Source
  KAKENHI-PROJECT-15K13431
[Presentation] Duality-singularity of indefinite metrics and contact structures2017
- Author(s)
  Goo Ishikawa
- Organizer
  24th Numazu conference,
- Place of Presentation
  沼津高専（静岡県・沼津市）
- Invited
- Data Source
  KAKENHI-PROJECT-15K13431
[Presentation] Stability of parametric Lagrangian and Legendrian varieties,2017
- Author(s)
  Goo Ishikawa
- Organizer
  International Conference on Singularity Theory and Dynamical Systems
- Int'l Joint Research / Invited
- Data Source
  KAKENHI-PROJECT-15K13431
[Presentation] Stability of parametric Lagrangian and Legendrian varieties2017
- Author(s)
  Goo Ishikawa
- Organizer
  International Conference on Singularity Theory and Dynamical Systems
- Int'l Joint Research / Invited
- Data Source
  KAKENHI-PROJECT-15H03615
[Presentation] Duality-singularity of indefinite metrics and contact structures2017
- Author(s)
  Goo Ishikawa
- Organizer
  Singularities in Generic Geometry and its Applications
- Int'l Joint Research / Invited
- Data Source
  KAKENHI-PROJECT-15H03615
[Presentation] Duality-singularity of indefinite metrics and contact structures2017
- Author(s)
  Goo Ishikawa
- Organizer
  Contact structure, Singularities, Differential equations and related area
- Place of Presentation
  金沢大学サテライト（石川県・金沢市）
- Data Source
  KAKENHI-PROJECT-15K13431
[Presentation] アフィン接続と空間曲線の接線曲面の特異点2016
- Author(s)
  石川剛郎，山下達也
- Organizer
  日本数学会2016年度年会
- Place of Presentation
  筑波大学（茨城県・つくば市）
- Year and Date
  2016-03-18
- Data Source
  KAKENHI-PROJECT-15K13431
[Presentation] Null frontal singular surfaces in Lorentzian 3-spaces2016
- Author(s)
  Goo Ishikawa, Yoshinori Machida, Masatomo Takahashi
- Organizer
  VIII International Meeting on Lorentzian Geometry
- Place of Presentation
  マラガ（スペイン）
- Year and Date
  2016-09-20
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K13431
[Presentation] ニュートラル計量，ローリング・ボディ，そしてケプラー問題2016
- Author(s)
  石川剛郎
- Organizer
  第２３回沼津研究会
- Place of Presentation
  沼津工業高等専門学校（静岡県・沼津市）
- Year and Date
  2016-03-08
- Invited
- Data Source
  KAKENHI-PROJECT-15K13431
[Presentation] 特異点論の地図2016
- Author(s)
  石川剛郎
- Organizer
  Encounter with Mathematics
- Place of Presentation
  中央大学理工学部（東京都・文京区）
- Year and Date
  2016-03-12
- Invited
- Data Source
  KAKENHI-PROJECT-15H03615
[Presentation] アフィン接続と空間曲線の接線曲面の特異点2016
- Author(s)
  石川剛郎，山下達也
- Organizer
  日本数学会2016年度年会
- Place of Presentation
  筑波大学（茨城県・つくば市）
- Year and Date
  2016-03-18
- Data Source
  KAKENHI-PROJECT-15H03615
[Presentation] Null frontal singular surfaces in Lorentzian 3-spaces2016
- Author(s)
  Goo Ishikawa
- Organizer
  VIII International Meeting on Lorentzian Geometry
- Place of Presentation
  マラガ（スペイン）
- Year and Date
  2016-09-20
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15H03615
[Presentation] 特異点論の地図2016
- Author(s)
  石川剛郎
- Organizer
  Encounter with Mathmatics
- Place of Presentation
  中央大学理工学部（東京都・文京区）
- Year and Date
  2016-03-12
- Invited
- Data Source
  KAKENHI-PROJECT-15K13431
[Presentation] ニュートラル計量，ローリング・ボディ，そしてケプラー問題2016
- Author(s)
  石川剛郎
- Organizer
  第２３回沼津研究会
- Place of Presentation
  沼津工業高等専門学校（静岡県・沼津市）
- Year and Date
  2016-03-08
- Invited
- Data Source
  KAKENHI-PROJECT-15H03615
[Presentation] Leibniz complexity of Nash functions on differentiations2015
- Author(s)
  Goo Ishikawa
- Organizer
  Geometric Singularity Theory, Polish-Japanese Singularity Theory Working Days
- Place of Presentation
  Warsaw (Poland)
- Year and Date
  2015-09-09
- Int'l Joint Research / Invited
- Data Source
  KAKENHI-PROJECT-15K13431
[Presentation] Leibniz complexity of Nash functions on differentiations2015
- Author(s)
  Goo Ishikawa
- Organizer
  Geometric Singularity Theory, Polish-Japanese Singularity Theory Working days
- Place of Presentation
  Warsaw (Poland)
- Year and Date
  2015-09-09
- Int'l Joint Research / Invited
- Data Source
  KAKENHI-PROJECT-26287009
[Presentation] Leibniz complexity of Nash functions on differentiations2015
- Author(s)
  Goo Ishikawa
- Organizer
  Geometric Singularity Theory, Polish-Japanese Singularity Theory Working Days
- Place of Presentation
  Warsaw (Poland)
- Year and Date
  2015-09-09
- Int'l Joint Research / Invited
- Data Source
  KAKENHI-PROJECT-15H03615
[Presentation] Affine connections and singularities of tangent surfaces to space curves2014
- Author(s)
  Goo Ishikawa
- Organizer
  Singularity theory of differential maps and its applications
- Place of Presentation
  京都大学数理解析研究所（京都市）
- Year and Date
  2014-12-05
- Invited
- Data Source
  KAKENHI-PROJECT-26287009
[Presentation] 幾何学的制御理論から観たCartan 分布の特異パス双対性2013
- Author(s)
  石川剛郎
- Organizer
  日本数学会秋季総合分科会
- Place of Presentation
  愛媛大学(松山市), 日本
- Year and Date
  2013-09-24
- Data Source
  KAKENHI-PROJECT-23654058
[Presentation] The D4-triality and singularities of tangent surfaces2013
- Author(s)
  Goo Ishikawa
- Organizer
  Singularities in geometry and applications III
- Place of Presentation
  The International Centre for Mathematical Sciences (ICMS), Edinburgh, Scotland, UK.
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] Singular path duality for Cartan distributions from geometric control theory (in Japanese)2013
- Author(s)
  Goo Ishikawa, Yumiko Kitagawa, Wataru Yukuno
- Organizer
  Autumn Meeting 2013 of Mathematical Society of Japan
- Place of Presentation
  Ehime University, Ehime Japan
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] 幾何学的制御理論から観たCartan 分布の特異パス双対性2013
- Author(s)
  石川剛郎
- Organizer
  日本数学会
- Place of Presentation
  愛媛大学（松山市）
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] The D4-triality and singularities of tangent surfaces2013
- Author(s)
  G. Ishikawa
- Organizer
  Singularities in geometry and applications III
- Place of Presentation
  ICMS, Edinburgh, Scotland, UK.
- Invited
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] 幾何学的制御理論から観たCartan 分布の特異パス双対性2013
- Author(s)
  石川剛郎
- Organizer
  日本数学会
- Place of Presentation
  愛媛大学（松山市）
- Data Source
  KAKENHI-PROJECT-23654058
[Presentation] Singular path duality for Cartan distributions from geometric control theory2013
- Author(s)
  Goo Ishikawa
- Organizer
  Geometric Singularity Theory, 8th Polish-Japanese Singularity Theory Working Days
- Place of Presentation
  The Banach Center, IMPAN, Warsaw, Poland
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] Singularities of Tangent Surfaces in Cartan’s Split G2-geometry2012
- Author(s)
  Goo Ishikawa
- Organizer
  The V-th International Conference of Differential Geometry and Dynamical Systems
- Place of Presentation
  Mangalia, Romania
- Invited
- Data Source
  KAKENHI-PROJECT-22244004
[Presentation] Shyuichi Izumiya’s mathematical works2012
- Author(s)
  Goo Ishikawa
- Organizer
  The 12th International Workshop on Real and Complex Singularities
- Place of Presentation
  Sao Carlos, Brazil
- Invited
- Data Source
  KAKENHI-PROJECT-22244004
[Presentation] Singularities of tangent surfaces in G2-geometric structures2012
- Author(s)
  Goo Ishikawa
- Organizer
  Singularities and Geometric Structures
- Place of Presentation
  長野市生涯学習センター（長野県）
- Invited
- Data Source
  KAKENHI-PROJECT-22244004
[Presentation] Tangent varieties and openings of map-germs2012
- Author(s)
  Goo Ishikawa
- Organizer
  An international workshop in Singularity Theory, its Applications and Future Prospects celebrating jubilees of Bill Bruce and Terry Wall
- Place of Presentation
  Liverpool, UK
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] Singularities of Tangent Surfaces in Cartan's Split G2-geometry2012
- Author(s)
  Goo Ishikawa
- Organizer
  The V-th International Conference of Differential Geometry and Dynamical Systems (DGDS-2012)
- Place of Presentation
  Mangalia, Romania
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] Openings of stable unfoldings2012
- Author(s)
  G.Ishikawa
- Organizer
  AMS Sectional Meeting, Special Session on Singularities, Stratifications and Their Applications
- Place of Presentation
  ハワイ大学マノア校(アメリカ)
- Year and Date
  2012-03-03
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] Singularities of tangent surfaces in G2-geometric structures2012
- Author(s)
  Goo Ishikawa
- Organizer
  Singularities and Geometric Structures
- Place of Presentation
  Lifelong Learning Center of Nagano City, Nagano, Japan
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] Tangent varieties and openings of map-germs2012
- Author(s)
  Goo Ishikawa
- Organizer
  An international workshop in Singularity Theory, its Applications and Future Prospects
- Place of Presentation
  Liverpool, UK
- Invited
- Data Source
  KAKENHI-PROJECT-22244004
[Presentation] Openings of stable unfoldings2012
- Author(s)
  Goo Ishikawa
- Organizer
  AMS Sectional Meeting, Special Session on Singularities, Stratifications and Their Applications
- Place of Presentation
  University of Hawaii at Manoa, Honolulu, HI, USA.
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] Singularities of Tangent Surfaces in Cartan's Split G2-geometry2012
- Author(s)
  Goo Ishikawa
- Organizer
  The V-th International Conference of Differential Geometry and Dynamical Systems
- Place of Presentation
  Callatis High-School, Mangalia (Romania)
- Year and Date
  2012-08-30
- Invited
- Data Source
  KAKENHI-PROJECT-23654058
[Presentation] Openings of stable unfoldings2011
- Author(s)
  Goo Ishikawa
- Organizer
  The 4th Japanese-Australian Workshop on Real and Complex Singularities
- Place of Presentation
  Kobe Satellite of Hyogo University of Teacher Education, Kobe, Japan.
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] Openings of stable unfoldings2011
- Author(s)
  Goo Ishikawa
- Organizer
  RIMS workshop, Singularity theory, geometry and topology
- Place of Presentation
  Kyoto, Japan
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] Singularities of Tangent Varieties to Curves and Surfaces2011
- Author(s)
  Goo Ishikawa
- Organizer
  Workshop on Singularities in Geometry and Applications
- Place of Presentation
  Stefan Banach International Mathematical Center, Bedlewo, Poland
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] Singularities of Tangent Varieties and Differential Systems2011
- Author(s)
  Goo Ishikawa
- Organizer
  Singularity Theory and its Applications
- Place of Presentation
  Academic Hall, Oita National College of Technology, Oita, Japan.
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] Basic topics on tropical geometry and singularities.2010
- Author(s)
  Goo Ishikawa
- Organizer
  Geometry on Real Closed Field and its Application to Singularity Theory
- Place of Presentation
  京都大学数理解析研究所招待講演
- Year and Date
  2010-11-30
- Data Source
  KAKENHI-PROJECT-22340030
[Presentation] Generic bifurcations of framed curves in a space form and their envelopes2010
- Author(s)
  G.Ishikawa
- Organizer
  Conatact structures, singularities, differential equations
- Place of Presentation
  洞爺湖文化センター,洞爺湖町,北海道
- Year and Date
  2010-01-27
- Data Source
  KAKENHI-PROJECT-21654008
[Presentation] Singularities of Framed Curves, Differential Systems, Projective Duality.2010
- Author(s)
  Goo Ishikawa
- Organizer
  11th International Workshop on Real, Complex Singularities
- Place of Presentation
  サンパウロ大学サンカルロス校(ブラジル、サンカルロス) 招待講演
- Year and Date
  2010-07-28
- Data Source
  KAKENHI-PROJECT-21654008
[Presentation] Introduction to Tropical Geometry2010
- Author(s)
  G.Ishikawa
- Organizer
  Kobe Workshop on Singularities
- Place of Presentation
  神戸サテライト,兵庫教育大学,兵庫
- Year and Date
  2010-01-20
- Data Source
  KAKENHI-PROJECT-21654008
[Presentation] Generic geometry and singularities of curves on surfaces2009
- Author(s)
  G.Ishikawa
- Organizer
  Durham Geometric Seminar
- Place of Presentation
  ダーラム大学,ダーラム,イギリス
- Year and Date
  2009-10-22
- Data Source
  KAKENHI-PROJECT-21654008
[Presentation] Singularity problems in sub-Riemannian and sub-Finsler2009
- Author(s)
  G.Ishikawa
- Organizer
  The 44-th Symposium on Finsler Geometry
- Place of Presentation
  東海大学札幌キャンパス,札幌,北海道
- Year and Date
  2009-09-09
- Data Source
  KAKENHI-PROJECT-21654008
[Presentation] Symplectic Invariants of Parametric Singularities Geometric Singularity Theory2009
- Author(s)
  G.Ishikawa
- Organizer
  7th Polish-Japanese Singularity Theory Working Days
- Place of Presentation
  カジミエッシュ・ドルニ,ポーランド
- Year and Date
  2009-07-14
- Data Source
  KAKENHI-PROJECT-21654008
[Presentation] Symplectic Invariants of Parametric Singularities2009
- Author(s)
  G.Ishikawa
- Organizer
  Real and Complex Singularities
- Place of Presentation
  シドニー大学、オーストラリア
- Year and Date
  2009-09-16
- Data Source
  KAKENHI-PROJECT-21654008
[Presentation] Geometry of surfaces with boundaries from singularity viewpoint2009
- Author(s)
  G.Ishikawa
- Organizer
  School on Generic Singularities in Geometry
- Place of Presentation
  バナッハセンター,ワルシャワ,ポーランド
- Year and Date
  2009-07-10
- Data Source
  KAKENHI-PROJECT-21654008
[Presentation] Classification of parametric varieties in the symplectic space:Motivations, Examples and Problems2008
- Author(s)
  G. Ishikawa
- Organizer
  10th International Workshop on Real and Compex Singularities
- Place of Presentation
  Sao Carlos, Brazil
- Year and Date
  2008-07-31
- Data Source
  KAKENHI-PROJECT-17340013
[Presentation] focalsymplecfic mvariants of parametric Lagrangian narieties2008
- Author(s)
  Goo ISHIKAWA
- Organizer
  Frobenius struefures and saigalanty thery
- Place of Presentation
  ポランド・ベドレボ
- Year and Date
  2008-08-26
- Data Source
  KAKENHI-PROJECT-19654006
[Presentation] Local symplectic invariants of parametric Lagrangian varieties2008
- Author(s)
  G. Ishikawa
- Organizer
  Frobenius structures and singularity theory
- Place of Presentation
  Bedlewo, Poland
- Year and Date
  2008-08-26
- Data Source
  KAKENHI-PROJECT-17340013
[Presentation] Local classification of varieties in the symplectic space2007
- Author(s)
  G. Ishikawa
- Organizer
  The second Japanese-Australian Workshop on Real and Complex Smgularities
- Place of Presentation
  京都大学数理解析研究所
- Year and Date
  2007-11-26
- Data Source
  KAKENHI-PROJECT-19654006
[Presentation] Local classification of parametric Lagrangian varieties2007
- Author(s)
  G. Ishikawa
- Organizer
  Internation Conference "Symplectic Geometry"
- Place of Presentation
  京都大学数理解析研究所
- Year and Date
  2007-07-27
- Data Source
  KAKENHI-PROJECT-17340013
[Presentation] Calssification problem in symplectic singularity theory2007
- Author(s)
  G. Ishikawa
- Organizer
  Banach Center Symposium "Geometric SingularityTheory" Polish-Japanese Working Days
- Place of Presentation
  Sopot, Poland
- Year and Date
  2007-07-09
- Data Source
  KAKENHI-PROJECT-17340013
[Presentation] Calssification problem in symplectic singularity theory2007
- Author(s)
  G. Ishikawa
- Organizer
  Banach Center Symposium "Geometric Singularity Theory" Polish-Japanese Working Days,
- Place of Presentation
  Sopot, Poland.
- Year and Date
  2007-07-09
- Data Source
  KAKENHI-PROJECT-17340013

1. IZUMIYA Shyuichi (80127422)

# of Collaborated Projects : 36results

# of Collaborated Products : 7results
2. YAMAGUCHI Keizo (00113639)

# of Collaborated Projects : 23results

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3. TATSUO Suwa (40109418)

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4. NAKAI Isao (90207704)

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5. ONO Kaoru (20204232)

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6. KIYOHARA Kazuyoshi (80153245)

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8. OHMOTO Toru (20264400)

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9. OKA Mutsuo (40011697)

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10. MORIMOTO Tohru (80025460)

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11. UMEHARA Masaaki (90193945)

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12. SATO Hajime (30011612)

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14. NAKAMURA Iku (50022687)

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15. MACHIDA Yoshinori (90141895)

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16. KAWASUMI Nariya (30214646)

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17. TAKAHASHI Masatomo (80431302)

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18. MIYAOKA Reiko (70108182)

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19. YAMADA Kotaro (10221657)

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20. AGAOKA Yoshio (50192894)

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21. MUTSUMI Saito (70215565)

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22. KOIKE Shigeaki (90205295)

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23. KENJI Fukaya (30165261)

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GO-O Ishikawa 石川 剛郎

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Developments and Applications of Geometric Singularity TheoryPrincipal InvestigatorOngoing

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Application of sub-Riemannian geometry to vision modelPrincipal Investigator

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Developments and applications of geometric singularity theoryPrincipal InvestigatorOngoing

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Floer 理論の深化と symplectic 構造の研究Ongoing

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The construction of infinite dimensional singularity theory of completely non-integrable systems and its applications to the singular motion-planning problemPrincipal Investigator

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The synthetic study by real algebraic geometry, from sub-Riemannian geometry to tropical geometryPrincipal Investigator

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GO-O Ishikawa 石川剛郎