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Kato, Tsuyoshi

Graduate School of Science, Division of Mathematics and Mathematical Sciences Professor

Kato, Tsuyoshi
list
    Last Updated :2023/01/24

    Basic Information

    Faculty

    • 理学部

    Academic Degree

    • 修士（数理科学）(東京大学)
    • 博士（理学）(京都大学)

    ID,URL

    researchmap URL

    list
      Last Updated :2023/01/24

      Research

      Research Topics, Overview of the research

      • Research Topics

        (1) Non compact geometric analysis
        (2) Non commutative geometry
        (3) Dynamical scale transform

      • Overview of the research

        Atiyah-Singer index theorem is a monumental theory in differential topology. Later around 2000 year, it has created two main streams where one is non linear moduli theory in topology and the other is the index theorem on non compact spaces. My research objective in (1) (2) is to construct moduli theory over non compact spaces by unifying these two subjects. Tropical geometry is a kind of dynamical scale transform, which is also called ultra-discretization, and the objective in (3) is to apply such scale transform to geometric objects such as automata groups.

      Research Areas

      • Natural sciences, Geometry

      Papers

      • Vector fields on non-compact manifolds
        Tsuyoshi Kato; Daisuke Kishimoto; Mitsunobu Tsutaya
        arXiv, Nov. 2022
      • Seiberg-Witten theory on finite covering spaces of spin 4-manifolds
        Tsuyoshi Kato; Doman Takata
        arXiv, Jan. 2022
      • L2 harmonic theory, Seiberg-Witten theory and asymptotic of differential forms
        Tsuyoshi Kato
        Journal of Gokova Geometry and Topology, Jan. 2022, Peer-reviewed, Lead author, Corresponding author
      • Hilbert bundles with ends
        Tsuyoshi Kato; Daisuke Kishimoto; Mitsunobu Tsutaya
        Journal of Topology and Analysis, online ready, 31 Dec. 2021, Peer-reviewed
      • Covering-monopole map and higher degree in non-commutative geometry
        Tsuyoshi Kato
        Journal of noncommutative geometry, 22 Nov. 2021, Peer-reviewed
      • Upper bounds for virtual dimensions of Seiberg-Witten moduli spaces
        Tsuyoshi Kato; Daisuke Kishimoto; Nobuhiro Nakamura; Kouichi Yasui
        arXiv, Nov. 2021
      • Induced map on K theory for certain \Gamma-equivariant maps between Hilbert spaces
        Tsuyoshi Kato
        Journal of non commutative geometry, Nov. 2021, Peer-reviewed
      • Rigidity of the mod 2 families Seiberg–Witten invariants and topology of families of spin 4-manifolds
        Tsuyoshi Kato; Hokuto Konno; Nobuhiro Nakamura
        Compositio Mathematica, Apr. 2021, Peer-reviewed
      • Homotopy type of the unitary group of the uniform Roe algebra on Z^n
        Tsuyoshi Kato; Daisuke Kishimoto; Mitsunobu Tsutaya
        Journal of Topology and Analysis, online ready, Mar. 2021, Peer-reviewed
      • Twisted Donaldson invariants
        TSUYOSHI KATO; HIROFUMI SASAHIRA; HANG WANG
        Mathematical Proceedings of the Cambridge Philosophical Society, Feb. 2021, Peer-reviewed
      • A note on exotic families of 4-manifolds
        T. Kato; H. Konno; N. Nakamura
        Proceedings of the AMS, Nov. 2022, Peer-reviewed
      • The simple type conjecture for mod 2 Seiberg-Witten invariants
        T. Kato; N. Nakamura; K. Yasui
        Journal of the European Mathematical Society, Jan. 2021, Peer-reviewed
      • Homotopy types of spaces of finite propagation unitary operators on Z
        T. Kato; D. Kishimoto; M. Tsutaya
        Homotopy, homology and applications (accepted), Oct. 2022, Peer-reviewed
      • DYNAMICS OF THE BOX-BALL SYSTEM WITH RANDOM INITIAL CONDITIONS VIA PITMAN’S TRANSFORMATION
        D.Croydon; T.Kato; M.Sasada; S.Tsujimoto
        Memoir of AMS (accepted), 2020, Peer-reviewed
      • Higher Nahm transform in non commutative geometry
        T. Kato; H. Sasahira; H. Wang
        arXiv, Jul. 2018
      • Spectral Analysis of Transition Operators, Automata Groups and Translation in BBS
        Tsuyoshi Kato; Satoshi Tsujimoto; Andrzej Zuk
        COMMUNICATIONS IN MATHEMATICAL PHYSICS, Feb. 2017, Peer-reviewed
      • Automata in Groups and Dynamics and Induced Systems of PDE in Tropical Geometry
        Tsuyoshi Kato
        JOURNAL OF GEOMETRIC ANALYSIS, Apr. 2014, Peer-reviewed
      • Automata groups and box-ball systems
        S. Tsujimoto; T. Kato; A. Zuk
        RIMS Kôkyûroku Bessatsu, 2014, Peer-reviewed
      • A note on the pentagram map and tropical geometry
        Tsuyoshi Kato
        arXiv, 2014
      • Localized ASD moduli spaces based on the reduced cohomology group over Casson handles
        Tsuyoshi Kato
        arXiv, 2013
      • An asymptotic complexity on Hamiltonian deformations and discrete groups acting on trees
        Tsuyoshi Kato
        arXiv, 2013
      • Asymptotically quasiconformal four manifolds
        Tsuyoshi Kato
        JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, Apr. 2012, Peer-reviewed
      • Infinite sequences of almost Kaehler manifolds with high symmetry, their perturbations and pseudo holomorphic curves
        Tsuyoshi Kato
        arXiv, 2012
      • Analytic relation on partial differential equations
        Tsuyoshi Kato; Satoshi Tsujimoto
        Journal of Mathematics Research, 2012, Peer-reviewed
      • An Asymptotic Comparison of Differentiable Dynamics and Tropical Geometry
        Tsuyoshi Kato
        MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, Mar. 2011, Peer-reviewed
      • Pattern formation from projectively dynamical systems and iterations by families of maps
        Tsuyoshi Kato
        PROBABILISTIC APPROACH TO GEOMETRY, 2010, Peer-reviewed
      • Geometric representations of interacting maps
        Tsuyoshi Kato
        International Journal of Mathematics and Mathematical Sciences, 2010, Peer-reviewed
      • Deformations of Real Rational Dynamics in Tropical Geometry
        Tsuyoshi Kato
        GEOMETRIC AND FUNCTIONAL ANALYSIS, Dec. 2009, Peer-reviewed
      • Dynamical scale transform and interaction graphs
        加藤 毅
        数理解析研究所講究録, 2009
      • Growth of Casson handles and transversality for ASD moduli spaces
        Tsuyoshi Kato
        GEOMETRY & TOPOLOGY, 2008, Peer-reviewed
      • Entropy comparisons and codings on interacting maps
        Tsuyoshi Kato
        Kyoto Univ. preprint, 2006
      • Interaction states by iterating maps in molecular biology
        Tsuyoshi Kato
        数理解析研究所講究録, 2005
      • Interacting maps, symbolic dynamics and automorphisms in microscopic scale
        Tsuyoshi Kato
        Int. Journal of Pure and Applied Mathematics, 2005, Peer-reviewed
      • Operator dynamics in molecular biology
        T Kato
        ADVANCES IN NATURAL COMPUTATION, PT 2, PROCEEDINGS, 2005, Peer-reviewed
      • Spectral analysis on tree like spaces from gauge theoretic view points
        Tsuyoshi Kato
        Contemporary Mathematics (AMS), 2004, Peer-reviewed, Invited
      • ASD moduli spaces over four-manifolds with tree-like ends
        T Kato
        GEOMETRY & TOPOLOGY, 2004, Peer-reviewed
      • Asymptotic Lipschitz maps, combable groups and higher signatures
        T Kato
        GEOMETRIC AND FUNCTIONAL ANALYSIS, 2000, Peer-reviewed
      • The asymptotic method in the Novikov conjecture
        Tsuyoshi Kato
        Sci. Bull. Josai University, Special Issue, 1997, Peer-reviewed, Invited
      • Asymptotic Lipschitz cohomology and higher signatures
        T Kato
        GEOMETRIC AND FUNCTIONAL ANALYSIS, 1996, Peer-reviewed

      Presentations

      • L2 harmonic theory and Seiberg-Witten, Bauer-Furuta theory on non-compact com- plete Riemannian 4-manifolds
        T. Kato
        SouthamptonKyoto Workshop 2, 07 Dec. 2020, Invited
      • Homotopy types of spaces of finite propagation unitary operators on Z
        M. Tsutaya
        Unitary operators:spectral and topological properties, 29 Sep. 2020, Invited
      • L^2 harmonic theory and Seiberg-Witten・Bauer-Furuta theory on non-compact complete Riemannian 4-manifolds
        T. Kato
        The Eighth Pacific Rim Conference in Mathematics, Session on Differential Geometry, 06 Aug. 2020, Invited
      • Some development of Seiberg-Witten theory and related topics
        Tsuyoshi Kato
        Southampton-Kyoto Workshop, 10 Sep. 2019, Invited
      • Some development of Seiberg-Witten theory and related topics
        Tsuyoshi Kato
        Geometry Symposium, 29 Aug. 2019, Invited
      • A rigidity theorem of the Z_2-valued Seiberg-Witten invariants for spin families
        Tsuyoshi Kato
        http://www.math.nus.edu.sg/~mathanf/Meeting-2019.06/IndexDual.html, 17 Jun. 2019, Invited
      • Twisted Donaldson invariant
        Tsuyoshi Kato
        http://www.scms.fudan.edu.cn/Data/View/1253.html, 03 Jun. 2019, Invited
      • Non commutative geometry and gauge theory
        Tsuyoshi Kato
        Geometry, Analysis, Groups, 01 Oct. 2018, Invited
      • Twisted Donaldson invariant
        Tsuyoshi Kato
        Gauge theory and applications at Reurggensg, 27 Jul. 2018, Invited
      • Twisted Donaldson invariant
        Tsuyoshi Kato
        Colloquium talk at UNSW, 29 Jun. 2018, Invited
      • Higher Nahm transform in non commutative geometry
        Tsuyoshi Kato
        https://www.osaka-med.ac.jp/deps/mat/nakamura/kgs/index.html, 19 May 2018
      • Higher Nahm transform in non commutative geometry
        Tsuyoshi Kato
        Workshop on Non Commutative Geometry and Representation Theory, 15 May 2018, Invited
      • Higher Nahm transform in non commutative geometry
        Tsuyoshi Kato
        2018 Spring operator algebra program at ECNU, 09 Apr. 2018, Invited
      • Twisted Donaldson invariant
        Tsuyoshi Kato
        Topology/Geometry lectures at Seoul National Univ, 19 Mar. 2018, Invited
      • Twisted Donaldson invariant
        Tsuyoshi Kato
        Non commutative geometry seminar at Pennsilvania State University, 08 Feb. 2018, Invited
      • Higher degree of the covering monopole map in non commutative geometry
        Tsuyoshi Kato
        Math of Gauge fields, Simons Center for Geometry and Physics, 31 Mar. 2017, Invited
      • Covering monopole map in non commutative geometry
        Tsuyoshi Kato
        NCG Shanghai 2017, Connes 70 anniversary, 24 Mar. 2017, Invited
      • Covering monopole map and its applications
        Tsuyoshi Kato
        TITECH Geometry seminar, 27 Jan. 2017, Invited
      • Higher degree of the covering monopole map and its computation 1,2,3
        Tsuyoshi Kato
        Geometric Analysis in Geometry and Topology 2016, 12 Dec. 2016, Invited
      • Higher degree of the covering monopole map in four manifold theory
        Tsuyoshi Kato
        Perspectives and Challenges in Mathematical Sciences, 01 Oct. 2016, Invited
      • K-theoretic degree of the covering monopole map
        Tsuyoshi Kato
        Geometry seminar at Vanderbilt University, 25 Sep. 2015, Invited
      • Non linear analysis over infinite dimensional spaces and its applications
        Tsuyoshi Kato
        Cooloqium talk at University of Adelaide, 06 Feb. 2015, Invited
      • Spectral coincidence between automata groups and BBS in tropical geometry
        Tsuyoshi Kato
        Geometry and physics seminar at Penn-State University, 02 Sep. 2014, Invited
      • Spectral coincidence of transition operators between automata groups and BBS in tropical geometry
        Tsuyoshi Kato
        Special week on operator algebras, 04 Aug. 2014, Invited
      • Spectral coincidence between lamplighter and BBS automata
        Tsuyoshi Kato
        Seminaire Algebres d'opérateurs at Universite Paris 7, 26 Sep. 2013, Invited
      • Spectral coincidence between lamplighter and BBS automata
        Tsuyoshi Kato
        Colloqium talk at La Saienza, Italy, 10 Sep. 2013, Invited
      • Hamiltonian deformation of groups acting on trees
        Tsuyoshi Kato
        11-th annual spring institute on non commutative geometry and operator algebras, 08 May 2013, Invited
      • A rough analytic relation on partial differential equations
        Tsuyoshi Kato
        China Japan joint workshop on integrable systems, 16 Mar. 2013, Invited
      • Hamiltonian deformation of groups acting on trees
        Tsuyoshi Kato
        Colloqium talk at Universite Paris 7, 13 Dec. 2012, Invited
      • Moduli spaces of holomorphic curves over infinite dimensional spaces
        Tsuyoshi Kato
        The 8-th China-Japan Friendship Conference on differential geometry, 11 Sep. 2012, Invited
      • Moduli theory over infinite dimensional spaces
        Tsuyoshi Kato
        Geometry and Analysis at Universite Paris 7, Sep. 2012, Invited
      • Automata groups and tropical geometry
        Tsuyoshi Kato
        International Conference on Groups, Dynamics and Random Structures at Texas A&M, USA, 24 Mar. 2012, Invited
      • Automata groups, tropical geometry and dynamical Burnside problem
        Tsuyoshi Kato
        Seminar on geometry, Universite Paris 7, Dec. 2011, Invited
      • Dynamical Burnside Problem
        Tsuyoshi Kato
        Seminar on groups, Vanderbilt University, Nov. 2011, Invited
      • Dynamical Burnside Problem
        加藤 毅
        仙台シンポジウム, Aug. 2011, Invited
      • Hyperbolic systems of PDEs and automata groups in tropical geometry
        Tsuyoshi Kato
        Workshop on automata groups and non commutative geometry, Universite Paris 7, France, Mar. 2011, Invited
      • Hyperbolic systems of PDEs and automata groups in tropical geometry
        Tsuyoshi Kato
        International workshop Geometry and Analysis, Universite Paris 7, France, Dec. 2010, Invited
      • A rough analytic relation on the set of PDE
        Tsuyoshi Kato
        Long-term workshop: Mathematical Sciences and Their Applications（上諏訪）, Sep. 2010, Invited
      • Casson handles and smooth structure on 4-manifolds
        Tsuyoshi Kato
        Colloquium at University of Sourthen California (USA), Sep. 2010, Invited
      • Automata groups and PDE in tropical geometry
        Tsuyoshi Kato
        Geometry and probability（東北大学）, Aug. 2010
      • Casson handles and gauge theory
        Tsuyoshi Kato
        Pacific Rim Conference, Stanford University, USA, Jun. 2010, Invited
      • Growth of Casson handles and smooth structure on 4-manifolds
        Tsuyoshi Kato
        Colloquium at Fudan University, China, Jun. 2010, Invited

      Books and Other Publications

      Awards

      • 1995
        井上財団, 井上研究奨励賞
      • 1996
        日本数学会, 日本数学会建部賢弘賞
      • 2006
        文部科学省, 文部科学大臣表彰若手科学者賞

      External funds: Kakenhi

      • Analysis of discrete Integrable systems by probability theory based on Pitman's transformation
        Grant-in-Aid for Scientific Research (B)
        Basic Section 12010:Basic analysis-related
        Kyoto University
        辻本 諭
        From 01 Apr. 2019, To 31 Mar. 2024, Granted
        離散可積分系;確率論;Pitman変換;箱玉系
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19H01792/
      • Pentagram map in tropical geometry and its application to discrete Morse theory
        Grant-in-Aid for Challenging Research (Exploratory)
        Kyoto University
        Tsuyoshi Kato
        From 30 Jun. 2017, To 31 Mar. 2020, Project Closed
        トロピカル幾何学;力学系;Pitman変換;Nahm変換;量子ランダムウオーク;ホモトピー型;箱玉系;ピットマン変換;Pentagram写像;離散モース理論
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17K18725/
      • 指数定理の展開とトポロジカル表面状態
        Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
        Science and Engineering
        The University of Tokyo
        古田 幹雄
        From 30 Jun. 2017, To 31 Mar. 2022, Project Closed
        指数定理;バルクエッジ対応;格子指数定理;ドメインウォール;トポロジー;Bott周期性;K群;スペクトル切断;Wilson-Dirac作用素;ゲージ理論
        https://kaken.nii.ac.jp/grant/KAKENHI-PLANNED-17H06461/
      • Construction of the covering monopole map and its applications
        Grant-in-Aid for Scientific Research (B)
        Kyoto University
        加藤 毅
        From 01 Apr. 2017, To 31 Mar. 2021, Granted
        サイバーグ・ウイッテン理論;非可換幾何学;Bauer-Furuta理論;K理論;バウアー・古田理論;ファイバー束;調和振動子;有限伝搬ユニタリ作用素;特性類;サイバーグ・ウィッテン理論;Bauer-Fruta理論;無限群;ゲージ理論;被覆モノポール写像;無限次元Bott周期性
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17H02841/
      • Various invariants of 3 and 4-manifolds and their applicationsUe
        Grant-in-Aid for Scientific Research (C)
        Kyoto University
        Masaaki Ue
        From 01 Apr. 2016, To 31 Mar. 2020, Project Closed
        4次元多様体;3次元多様体;Seiberg-Witten理論;Floerホモロジー;ザイフェルト多様体;３次元多様体;ゲージ理論;ザイフェルト３次元多様体;Heegaard Floerホモロジー;低次元トポロジー;４次元多様体
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16K05146/
      • Theory of classical orthogonal polynomials in terms of discrete integrable systems and its applications
        Grant-in-Aid for Scientific Research (C)
        Kyoto University
        SATOSHI TSUJIMOTO
        From 01 Apr. 2013, To 31 Mar. 2016, Project Closed
        力学系・可積分系;直交多項式;特殊関数;古典直交多項式;例外型直交多項式;箱玉系;オートマトン;離散可積分系;国際研究者交流　ウクライナ
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-25400110/
      • Moduli theory of non linear elliptic operators over non compact manifolds
        Grant-in-Aid for Scientific Research (B)
        Kyoto University
        Tsuyoshi Kato
        From 01 Apr. 2013, To 31 Mar. 2017, Project Closed
        ゲージ理論;非可換幾何学;モノポール写像;普遍被覆空間;サイバーグウイッテン理論;無限次元ボット周期性;非コンパクト空間上の解析;Lpコホモロジー;離散群;スペクトル解析;モジュライ空間;キャッソンハンドル;非コンパクト多様体
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-25287009/
      • Relations between invariants of low-dimensional manifolds and their geometric structures
        Grant-in-Aid for Scientific Research (C)
        Kyoto University
        Masaaki Ue
        From 01 Apr. 2012, To 31 Mar. 2016, Project Closed
        低次元トポロジー;3次元多様体;4次元多様体;Seiberg-Witten理論;Heegaard Floerホモロジー;ザイフェルト多様体;ホモロジーコボルディズム;４次元多様体;３次元多様体;エータ不変量
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-24540076/
      • 非線形方程式のモジュライ空間の幾何学的応用
        Grant-in-Aid for Scientific Research (A)
        Kyoto University
        深谷 賢治
        From 01 Apr. 2011, To 31 Mar. 2012, Project Closed
        モジュライ空間;シンプレクティック幾何学;非線形微分方程式;ゲージ理論;フレアーホモロジー
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23244007/
      • Proof of Homological Mirror Symmetry
        Grant-in-Aid for Scientific Research (S)
        Kyoto University
        Kenji Fukaya
        From 01 Apr. 2011, To 31 Mar. 2016, Project Closed
        微分幾何学;位相幾何学;複素幾何学;代数幾何学;ミラー対称性;シンプレクティック幾何学;ラグランジュ部分多様体;仮想ホモロジー類;深谷圏;幾何学;代数学;解析学;シンプレクティック多様体;フレアーホモロジー
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23224002/
      • Research on systems of the biorthogonal functions, discrete andultradiscrete integrable systems, and their applications
        Grant-in-Aid for Scientific Research (C)
        Kyoto University
        Satoshi TSUJIMOTO
        From 01 Apr. 2010, To 31 Mar. 2013, Project Closed
        可積分系;離散可積分系;超離散可積分系;古典直交多項式;双直交関数系;一般化固有値問題;国際情報交換;アルゴリズム;応用数学;数理工学;直交多項式;量子力学
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540224/
      • Gauge theory with infinite group actions
        Grant-in-Aid for Scientific Research (C)
        Kyoto University
        Tsuyoshi KATO
        From 01 Apr. 2010, To 31 Mar. 2013, Project Closed
        無限群;非コンパクト幾何解析;スケール変換;概正則曲線;無限次元多様体;ハミルトン関数;ゲージ理論;力学系;非線形偏微分方程式;基本群;トロピカル幾何学
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540080/
      • A generalization of the Atiyah-Singer Index Theorem on Noncommutative manifolds
        Grant-in-Aid for Scientific Research (C)
        Nagoya University
        Hitoshi MORIYOSHI
        From 01 Apr. 2010, To 31 Mar. 2013, Project Closed
        指数定理;非可換幾何学;K理論;エータ不変量;葉層多様体;Godbillon-Vey類;巡回コホモロジー;非可換幾何;幾何学;位相幾何学;葉層構造;Godbillon-Vey不変量
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540077/
      • Topology of low dimensional manifolds with various geometric structures
        Grant-in-Aid for Scientific Research (C)
        Kyoto University
        Masaaki UE
        From 01 Apr. 2008, To 31 Mar. 2011, Project Closed
        微分トポロジー;3次元多様体;4次元多様体;Seiberg-Witten理論;不変量;ホモロジー3球面;フレアホモロジー;球面多様体;鉛管多様体;幾何学;トポロジー;Floerホモロジー;Seiber-Witten理論;有理ホモロジー3球面
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540072/
      • Noncommutative Geometry and equivariant index theorem for twisted group actions
        Grant-in-Aid for Scientific Research (C)
        Keio University
        Hitoshi MORIYOSHI
        From 01 Apr. 2007, To 31 Mar. 2010, Project Closed
        非可換幾何学;指数定理;K理論;エータ不変量;葉層構造;巡回コホモロジー;幾何学;位相幾何学;Godbillon-Vey不変量;国際研究者交流;イタリア:中国:アメリカ;接触構造;佐々木多様体
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540099/
      • gauge theory and homotopy theory
        Grant-in-Aid for Scientific Research (B)
        The University of Tokyo
        Mikio FURUTA
        From 01 Apr. 2007, To 31 Mar. 2011, Project Closed
        トポロジー;位相幾何;幾何学
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19340015/
      • Geometry of Moduli Spaces and its Application to Infinite Analysis
        Grant-in-Aid for Scientific Research (B)
        Tokyo Metropolitan University;Yokkaichi University;Kyoto University
        Kenji UENO
        From 01 Apr. 2007, To 31 Mar. 2011, Project Closed
        代数科学;共形場理論;モジュラー函手;位相的場の理論;タイヒミュラー;GNS構成法;ゲージ対称性;分岐被覆;剛幾何学;モジュライ空;無限可積分系;代数多様体の退化;重複ファイバー;トロピカル幾何学;変形パラメータ;導来圏;モジュライ空間;接続;ゲージ理論;代数曲線;退化;ユニタリ性;写像類群;射影的平坦接続;Hitchin接続;p進剛幾何学;ペンローズ変換
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19340007/
      • The study of Low-dimensicnal manifolds with various geometric structures
        Grant-in-Aid for Scientific Research (C)
        Kyoto University
        Masaaki UE
        From 01 Apr. 2006, To 31 Mar. 2008, Project Closed
        3次元多様体;4次元多様体;Seiberg-Witten理論;Heegaard Floerホモロジー;ホモロジー3球面;Floerホモロジー;ザイフェルト多様体;キャッソンハンドル;双曲構造, 3-manifold;4-manifold;Seiberg-Witten theory;Heegaard Floer homology;homology 3-sphere
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540081/
      • Non commutative geometry and moduli spaces of holomorphic curves
        Grant-in-Aid for Scientific Research (C)
        Kyoto University
        Tsuyoshi KATO
        From 01 Apr. 2006, To 31 Mar. 2010, Project Closed
        キャパシティー;モジュライ理論;非コンパクト空間;キャパシティ-;シンプレクティック幾何学;楕円型モジュライ空間;微分構造;シンプレクティック多様体;モジュライ空間
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540079/
      • New development of geometry based on topological field theory
        Grant-in-Aid for Scientific Research (S)
        Kyoto University
        Kenji FUKAYA
        From 01 Apr. 2006, To 31 Mar. 2011, Project Closed
        シンプレクティック多様体;ミラー対称性;フレアーホモロジー;シンプレクティク幾何;擬正則曲線;モジュライ空間;トーリック多様体;ハミルトン力学系;ラグランジュ部分多様体;シンプレクティック幾何学;量子コホモロジー;ミラ-対称性;フレア-ホモロジ-;カラビヤウ多様体;特異点理論;ホモロジー代数;超弦理論;幾何学;トポロジー;数理物理;素粒子論;解析学;弦理論
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18104001/
      • 非可換機何学における概正則曲線の研究
        Grant-in-Aid for Young Scientists (B)
        Kyoto University
        加藤 毅
        From 01 Apr. 2003, To 31 Mar. 2006, Project Closed
        キャパシティー;シンプレクティック多様体;KdVフロウ;無限次元多様体
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15740037/
      • Moduli space, Homotopical algebra, Field theory
        Grant-in-Aid for Scientific Research (S)
        Kyoto University
        Kenji FUKAYA
        From 01 Apr. 2001, To 31 Mar. 2006, Project Closed
        シンプレクティック幾何学;ラグランジュ部分多様体;フレアーホモロジー;ミラー対称性;A無限大構造;擬正則曲線;位相的場の理論;ハミルトン力学系;ループ空間;シンプレクティック微分同相群;曲率と基本群;open string;モジュライ空間;Dブレイン;A無限大代数;超ポテンシャル;Rigid幾何学;A無限代数;モース理論;ホモトピー代数, symplectic topology;Lagrangian sublmanifolds;Floer homology;Mirror symmetry;A infinity algebra;quasi-regular curve;Topological field theory;Hamiltonian dynamical system
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13852001/
      • 非可換ゲージ理論の研究
        Grant-in-Aid for Young Scientists (B)
        Kyoto University
        加藤 毅
        From 01 Apr. 2001, To 31 Mar. 2003, Project Closed
        無限次元シンプレクティック多様体;キャパシティー;非可換幾何学;ゲージ理論;シンプレクティック多様体
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13740037/
      • ノビコフ予想の研究
        Grant-in-Aid for Encouragement of Young Scientists (A)
        Kyoto University
        加藤 毅
        From 01 Apr. 1999, To 31 Mar. 2000, Project Closed
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11740040/
      • Moduli space and infinite dimensional geometry
        Grant-in-Aid for Scientific Research (A).
        KYOTO UNIVERSITY
        Kenji FUKAYA
        From 01 Apr. 1997, To 31 Mar. 2001, Project Closed
        シンプレクティック幾何;フレアーホモロジー;ホモトピー代数;モジュライ空間;ミラー対称性;概正則曲線;倉西写像;ラグランジュ部分多様体;シンプレクティック幾何学;対応;ハミルトン系;軌道体;テータ関数;アーベル多様体;非可換トーラス;フレア-ホモロジー;鏡映対称性;非可換幾何学;A無限大カテゴリー;ヤンミルズ方程式;テ-タ関数;マスロフ指数, Symplectic Geometry;Floer homology;Homotopical Algebra;moduli space;Mirror symmetry;pseudoholomorphic curve;Kuranishi map;Lagrangian submanifold
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09304008/
      • 高位の符号数のホモトピー不変性と無限離散群
        Grant-in-Aid for Encouragement of Young Scientists (A)
        Kyoto University
        加藤 毅
        From 01 Apr. 1996, To 31 Mar. 1997, Project Closed
        ノビコフ予想;無限離散群
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08740050/
      • 高位の符号数のホモトピー不変性
        Grant-in-Aid for Scientific Research on Priority Areas
        Kyoto University
        加藤 毅
        From 01 Apr. 1996, To 31 Mar. 1997, Project Closed
        符号数;Lジーナス;負曲率空間;C^+環
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08211233/
      • サイバーグ・ウイッテン理論の進化と4次元微分トポロジーへの応用
        Grant-in-Aid for Scientific Research (B)
        Basic Section 11020:Geometry-related
        Kyoto University
        加藤 毅
        From 01 Apr. 2022, To 31 Mar. 2027, Granted
        サイバーグ・ウイッテン理論;微分トポロジー;非コンパクト多様体
        https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22H01123/

      External funds: others

      • 日本学術振興会 最先端研究開発支援プログラム
        From 2010, To 2013
        加藤　毅/畑　政義
      list
        Last Updated :2023/01/24

        Education

        Teaching subject(s)

        • From 01 Apr. 2022, To 31 Mar. 2023
          Special study course (Mathematical Science)
          5140, Year-long, Faculty of Science, 12
        • From 01 Apr. 2022, To 31 Mar. 2023
          Seminar on Differential Geometry A
          0532, Spring, Graduate School of Science, 3
        • From 01 Apr. 2022, To 31 Mar. 2023
          Seminar on Geometry c
          0472, Spring, Graduate School of Science, 3
        • From 01 Apr. 2022, To 31 Mar. 2023
          Exercises in Geometry II
          3162, Fall, Faculty of Science, 4
        • From 01 Apr. 2022, To 31 Mar. 2023
          Seminar on Differential Geometry a
          0434, Spring, Graduate School of Science, 3
        • From 01 Apr. 2022, To 31 Mar. 2023
          Seminar on Geometry d
          0473, Fall, Graduate School of Science, 3
        • From 01 Apr. 2022, To 31 Mar. 2023
          Seminar on Differential Geometry B
          0533, Fall, Graduate School of Science, 3
        • From 01 Apr. 2022, To 31 Mar. 2023
          Seminar on Geometry b
          0471, Fall, Graduate School of Science, 3
        • From 01 Apr. 2022, To 31 Mar. 2023
          Seminar on Geometry a
          0470, Spring, Graduate School of Science, 3
        • From 01 Apr. 2022, To 31 Mar. 2023
          Seminar on Differential Geometry b
          0435, Fall, Graduate School of Science, 3
        • From 01 Apr. 2022, To 31 Mar. 2023
          Seminar on Differential Geometry d
          0437, Fall, Graduate School of Science, 3
        • From 01 Apr. 2022, To 31 Mar. 2023
          Seminar on Differential Geometry c
          0436, Spring, Graduate School of Science, 3
        • From Apr. 2011, To Mar. 2012
          数学と自然科学・社会科学Ⅰ
          Fall, 理学研究科
        • From Apr. 2011, To Mar. 2012
          数学と自然科学・社会科学Ⅱ
          Fall, 理学研究科
        • From Apr. 2011, To Mar. 2012
          数学と自然科学・社会科学Ⅲ
          Fall, 理学研究科
        • From Apr. 2011, To Mar. 2012
          数学基盤研究　幾何学A
          Spring, 理学研究科
        • From Apr. 2011, To Mar. 2012
          数学基盤研究　幾何学B
          Fall, 理学研究科
        • From Apr. 2011, To Mar. 2012
          Advanced Calculus A
          Spring, 全学共通科目
        • From Apr. 2011, To Mar. 2012
          幾何学演義II
          Fall, 理学部
        • From Apr. 2012, To Mar. 2013
          Geometry II
          Fall, 理学部
        • From Apr. 2012, To Mar. 2013
          Mathematics seminary
          Year-long, 理学部
        • From Apr. 2013, To Mar. 2014
          Exercises in Geometry I
          Spring, 理学部
        • From Apr. 2013, To Mar. 2014
          Calculus A
          Spring, 全学共通科目
        • From Apr. 2014, To Mar. 2015
          Set Theory & Topology
          Spring, 理学部
        • From Apr. 2014, To Mar. 2015
          Geometry II
          Fall, 理学部
        • From Apr. 2014, To Mar. 2015
          Mathematics and Natural Science, Social Science I
          Fall, 理学研究科
        • From Apr. 2014, To Mar. 2015
          Mathematics and Natural Science, Social Science II
          Fall, 理学研究科
        • From Apr. 2014, To Mar. 2015
          Mathematics and Natural Science, Social Science III
          Fall, 理学研究科
        • From Apr. 2014, To Mar. 2015
          Seminar on Differential Geometry A
          Spring, 理学研究科
        • From Apr. 2014, To Mar. 2015
          Seminar on Differential Geometry B
          Fall, 理学研究科
        • From Apr. 2014, To Mar. 2015
          Seminar on Differential Geometry C
          Spring, 理学研究科
        • From Apr. 2014, To Mar. 2015
          Seminar on Differential Geometry D
          Fall, 理学研究科
        • From Apr. 2014, To Mar. 2015
          Seminar on Geometry C
          Spring, 理学研究科
        • From Apr. 2014, To Mar. 2015
          Seminar on Geometry D
          Fall, 理学研究科
        • From Apr. 2014, To Mar. 2015
          Calculus A
          Spring, 全学共通科目
        • From Apr. 2014, To Mar. 2015
          Calculus B
          Fall, 全学共通科目
        • From Apr. 2015, To Mar. 2016
          Geometry II
          Fall, 理学部
        • From Apr. 2015, To Mar. 2016
          Seminar on Differential Geometry A
          Spring, 理学研究科
        • From Apr. 2015, To Mar. 2016
          Seminar on Differential Geometry B
          Fall, 理学研究科
        • From Apr. 2015, To Mar. 2016
          Seminar on Differential Geometry C
          Spring, 理学研究科
        • From Apr. 2015, To Mar. 2016
          Seminar on Differential Geometry D
          Fall, 理学研究科
        • From Apr. 2015, To Mar. 2016
          Calculus with Exercises A
          Spring, 全学共通科目
        • From Apr. 2015, To Mar. 2016
          Calculus with Exercises B
          Fall, 全学共通科目
        • From Apr. 2015, To Mar. 2016
          Seminar on Geometry A
          Spring, 理学研究科
        • From Apr. 2015, To Mar. 2016
          Seminar on Geometry B
          Fall, 理学研究科
        • From Apr. 2015, To Mar. 2016
          Set Theory & Topology
          Spring, 理学部
        • From Apr. 2016, To Mar. 2017
          Introduction to Geometry
          Fall, 理学部
        • From Apr. 2016, To Mar. 2017
          Exercises in Basic Geometry
          Fall, 理学部
        • From Apr. 2016, To Mar. 2017
          Seminar on Differential Geometry A
          Spring, 理学研究科
        • From Apr. 2016, To Mar. 2017
          Seminar on Differential Geometry B
          Fall, 理学研究科
        • From Apr. 2016, To Mar. 2017
          Seminar on Differential Geometry C
          Spring, 理学研究科
        • From Apr. 2016, To Mar. 2017
          Seminar on Differential Geometry D
          Fall, 理学研究科
        • From Apr. 2016, To Mar. 2017
          Seminar on Geometry C
          Spring, 理学研究科
        • From Apr. 2016, To Mar. 2017
          Seminar on Geometry D
          Fall, 理学研究科
        • From Apr. 2017, To Mar. 2018
          Introduction to Geometry
          Fall, 理学部
        • From Apr. 2017, To Mar. 2018
          Exercises in Basic Geometry
          Fall, 理学部
        • From Apr. 2017, To Mar. 2018
          Calculus with Exercises A
          Spring, 全学共通科目
        • From Apr. 2017, To Mar. 2018
          Seminar on Differential Geometry A
          Spring, 理学研究科
        • From Apr. 2017, To Mar. 2018
          Seminar on Differential Geometry B
          Fall, 理学研究科
        • From Apr. 2017, To Mar. 2018
          Seminar on Differential Geometry C
          Spring, 理学研究科
        • From Apr. 2017, To Mar. 2018
          Seminar on Differential Geometry D
          Fall, 理学研究科
        • From Apr. 2017, To Mar. 2018
          Mathematics seminary
          Year-long, 理学部
        • From Apr. 2018, To Mar. 2019
          Topology
          Spring, 理学部
        • From Apr. 2018, To Mar. 2019
          Graduate Lecture in Topology
          Spring, 理学研究科
        • From Apr. 2018, To Mar. 2019
          Seminar on Differential Geometry a
          Spring, 理学研究科
        • From Apr. 2018, To Mar. 2019
          Seminar on Differential Geometry b
          Fall, 理学研究科
        • From Apr. 2018, To Mar. 2019
          Seminar on Differential Geometry c
          Spring, 理学研究科
        • From Apr. 2018, To Mar. 2019
          Seminar on Differential Geometry d
          Fall, 理学研究科
        • From Apr. 2018, To Mar. 2019
          Mathematics seminary
          Year-long, 理学部
        • From Apr. 2019, To Mar. 2020
          Topology
          Spring, 理学部
        • From Apr. 2019, To Mar. 2020
          Graduate Lecture in Topology
          Spring, 理学研究科
        • From Apr. 2019, To Mar. 2020
          Seminar on Differential Geometry a
          Spring, 理学研究科
        • From Apr. 2019, To Mar. 2020
          Seminar on Differential Geometry b
          Fall, 理学研究科
        • From Apr. 2019, To Mar. 2020
          Seminar on Differential Geometry c
          Spring, 理学研究科
        • From Apr. 2019, To Mar. 2020
          Seminar on Differential Geometry d
          Fall, 理学研究科
        • From Apr. 2020, To Mar. 2021
          Topology
          Spring, 理学部
        • From Apr. 2020, To Mar. 2021
          Graduate Lecture in Topology
          Spring, 理学研究科
        • From Apr. 2020, To Mar. 2021
          Calculus with Exercises B
          Fall, 全学共通科目
        • From Apr. 2020, To Mar. 2021
          Seminar on Differential Geometry a
          Spring, 理学研究科
        • From Apr. 2020, To Mar. 2021
          Seminar on Differential Geometry b
          Fall, 理学研究科
        • From Apr. 2020, To Mar. 2021
          Seminar on Differential Geometry c
          Spring, 理学研究科
        • From Apr. 2020, To Mar. 2021
          Seminar on Differential Geometry d
          Fall, 理学研究科
        • From Apr. 2020, To Mar. 2021
          Special study course (Mathematical Science)
          Year-long, 理学部
        • From Apr. 2021, To Mar. 2022
          Geometry I
          Spring, 理学部
        • From Apr. 2021, To Mar. 2022
          Seminar on Differential Geometry a
          Spring, 理学研究科
        • From Apr. 2021, To Mar. 2022
          Seminar on Differential Geometry b
          Fall, 理学研究科
        • From Apr. 2021, To Mar. 2022
          Seminar on Differential Geometry c
          Spring, 理学研究科
        • From Apr. 2021, To Mar. 2022
          Seminar on Differential Geometry d
          Fall, 理学研究科
        • From Apr. 2021, To Mar. 2022
          Seminar on Geometry a
          Spring, 理学研究科
        • From Apr. 2021, To Mar. 2022
          Seminar on Geometry b
          Fall, 理学研究科
        • From Apr. 2021, To Mar. 2022
          Forefront of Mathematics and Mathematical Science II
          Fall, 理学部
        • From Apr. 2021, To Mar. 2022
          Special Lecture on Mathematics 10
          Year-long, 理学部
        • From Apr. 2021, To Mar. 2022
          Special Lecture on Mathematics 9
          Year-long, 理学部
        • From Apr. 2021, To Mar. 2022
          Linear Algebra with Exercises B
          Fall, 全学共通科目

        Participation in PhD Defense

        • A topological invariant for continuous fields of Cuntz algebras
          SOGABE TARO, Graduate School of Science, Sub-chief Examiner
          24 Nov. 2021
        list
          Last Updated :2023/01/24

          Administration

          School management (title, position)

          • From 01 Apr. 2022, To 31 Mar. 2023
            京都大学スーパーグローバルコース実施運営協議会 委員
          • From 20 Sep. 2009, To 31 Mar. 2011
            京都大学国際交流センター外国人留学生日本語・日本文化研修委員会 委員
          • From 01 Apr. 2011, To 31 Mar. 2014
            外国人留学生日本語・日本文化研修委員会 委員
          • From 01 Jul. 2011, To 30 Jun. 2013
            国際交流委員会 委員
          • From 19 Sep. 2013, To 31 Mar. 2014
            国際交流推進機構外国人留学生日本語・日本文化研修委員会
          • From 01 Jul. 2013, To 30 Jun. 2015
            国際交流委員会 委員
          • From 01 Jul. 2011, To 30 Jun. 2015
            国際交流委員会 委員
          • From 01 Apr. 2016, To 31 Mar. 2018
            国際教育委員会留学生受入専門委員会アジア未来リーダー育成奨学金プログラム小委員会 委員
          • From 01 Jun. 2016, To 31 Mar. 2018
            国際教育委員会国際学生交流委員会アジア未来リーダー育成奨学金プログラム小委員会 委員長
          • From 01 Apr. 2018, To 31 Mar. 2020
            アジア未来リーダー育成奨学金プログラム小委員会 委員
          • From 01 Apr. 2020, To 31 Mar. 2021
            国際高等教育院 企画評価専門委員会 数学部会 委員
          • From 01 Apr. 2021, To 31 Mar. 2022
            国際高等教育院 企画評価専門委員会 数学部会 委員
          • From 01 Apr. 2021
            スーパーグローバルコース企画運営幹事会 委員
          • From 01 Apr. 2021, To 31 Mar. 2022
            スーパーグローバルコース企画運営幹事会 協議員

          Faculty management (title, position)

          • From 01 Apr. 2022, To 31 Mar. 2023
            理学研究科将来計画委員会委員
          • From 01 Apr. 2014, To 31 Mar. 2015
            理学研究科自己点検・評価委員会委員
          • From 01 Apr. 2014, To 31 Mar. 2015
            理学研究科大学院教育教務委員会委員
          • From 01 Apr. 2014, To 31 Mar. 2015
            理学研究科国際・社会交流委員会委員長
          • From 01 Apr. 2014, To 01 May 2015
            理学研究科会議構成員
          • From 01 Apr. 2015, To 31 Mar. 2016
            理学研究科自己点検・評価委員会委員
          • From 01 Apr. 2015, To 31 Mar. 2016
            理学部・教育委員会委員
          • From 01 Apr. 2015, To 31 Mar. 2016
            理学研究科大学院教育教務委員会委員
          • From 01 Apr. 2014, To 31 Mar. 2015
            理学研究科会議構成員
          • From 01 Apr. 2015, To 30 Jun. 2015
            理学研究科国際・社会交流委員会委員長
          • From 01 Jul. 2015, To 31 Mar. 2016
            理学研究科国際・社会交流委員会委員長
          • From 01 Apr. 2015, To 31 Mar. 2016
            理学研究科国際・社会交流委員会　国際交流奨学生推薦小委員会委員
          • From 01 Apr. 2015, To 31 Mar. 2016
            理学研究科会議構成員
          • From 01 Apr. 2016, To 31 Mar. 2017
            理学部・教育委員会委員
          • From 01 Apr. 2016, To 31 Mar. 2017
            理学研究科国際・社会交流委員会委員
          • From 01 Apr. 2016, To 31 Mar. 2017
            理学研究科国際・社会交流委員会　国際交流奨学生推薦小委員会委員長
          • From 01 Apr. 2017, To 31 Mar. 2018
            理学研究科国際・社会交流委員会委員
          • From 01 Apr. 2017, To 31 Mar. 2018
            理学研究科国際・社会交流委員会　国際交流奨学生推薦小委員会委員
          • From 01 Apr. 2018, To 31 Mar. 2019
            理学研究科数学・数理解析専攻副専攻長
          • From 01 Apr. 2018, To 31 Mar. 2019
            理学研究科将来計画委員会委員
          • From 01 Apr. 2018, To 31 Mar. 2019
            理学研究科専攻長会議構成員
          • From 01 Apr. 2019, To 31 Mar. 2020
          • From 01 Apr. 2019, To 31 Mar. 2020
          • From 01 Apr. 2020, To 31 Mar. 2021
            理学部・教育委員会委員
          • From 01 Apr. 2020, To 31 Mar. 2021
            理学部・教育委員会　全学共通教育委員会委員
          • From 01 Apr. 2020, To 31 Mar. 2021
            理学部・教育委員会　少人数担任委員会委員
          • From 01 Apr. 2019, To 31 Mar. 2020
            理学研究科数学・数理解析専攻長
          • From 01 Apr. 2021, To 31 Mar. 2022
            理学部・教育委員会委員
          • From 01 Apr. 2021, To 31 Mar. 2022
            理学部・教育委員会　全学共通教育委員会委員
          • From 01 Apr. 2021, To 31 Mar. 2022
            理学部・教育委員会　入試専門小委員会委員
          • From 01 Apr. 2021, To 31 Mar. 2022
            理学部・教育委員会　少人数担任委員会委員
          • From 01 Apr. 2020, To 31 Mar. 2021
            国際高等教育院企画評価専門委員会分野別部会委員
          list
            Last Updated :2023/01/24

            Academic, Social Contribution

            Academic Contribution

            • Organizer of Global Non Commutative Geometry, Asia-Pasific region
              Planning, management, etc.
              https://globalncgseminar.org/organizers/

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