Updated on 2024/02/05

写真a

 
NAKAGAWA Masaki
 
Organization
Faculty of Education Professor
Position
Professor
External link

Degree

  • Doctor ( Kyoto University )

Research Interests

  • シューベルトカルキュラス

  • チャウ環

  • 等質空間

  • Lie群

  • 旗多様体

  • コホモロジー

  • homogeneous spaces

  • Lie groups

  • cohomology

  • flag manifolds

  • Chow rings

  • Schubert calculus

Research Areas

  • Natural Science / Geometry

Education

  • Kyoto University   大学院理学研究科   数学・数理解析専攻(数学)博士後期課程

    2000.4 - 2002.3

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    Country： Japan

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  • Kyoto University   大学院理学研究科   数学・数理解析専攻(数学)修士課程

    1998.4 - 2000.3

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  • Kyoto University   理学部   数学系

    1994.4 - 1998.3

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  • Kyoto University   工学部   機械系学科

    1991.4 - 1994.3

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Research History

  • Okayama University   Graduate School of Education   Associate Professor

    2012.4 - 2021.3

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  • Kagawa National College of Technology   Department of General Education   Associate Professor

    2011.10 - 2012.3

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  • Kagawa National College of Technology   Department of General Education   Lecturer

    2009.4 - 2011.9

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  • Takamatsu National College of Technology   一般教育課   Lecturer

    2003.4 - 2009.3

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  • JSPS (Japan Society for the Promotion of Science) Fellow

    2001.4 - 2003.3

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Professional Memberships

  • Mathematical Society of Japan

    2007.9

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Papers

  • The universal factorial Hall–Littlewood P- and Q-functions Reviewed International journal

    Masaki Nakagawa, Hiroshi Naruse

    FUNDAMENTA MATHEMATICAE   2023.8

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Instytut Matematyczny PAN  

    DOI： 10.4064/fm257-5-2023

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  • Darondeau–Pragacz formulas in complex cobordism Reviewed

    Masaki Nakagawa, Hiroshi Naruse

    Mathematische Annalen   2021.5

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    Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    DOI： 10.1007/s00208-021-02196-5

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    Other Link： https://link.springer.com/article/10.1007/s00208-021-02196-5/fulltext.html

  • On Heron's problem Reviewed

    Masaki Nakagawa

    ( 27 )   1 - 20   2021.3

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    Language：Japanese   Publishing type：Research paper (bulletin of university, research institution)  

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  • The mod 2 cohomology ring of the classifying space of the exceptional Lie group E_6 Reviewed

    Masaki Kameko, Masaki Nakagawa, Tetsu Nishimoto

    Proceedings of Japan Academy, Series A Mathematical Sciences   95 ( 9 )   91 - 96   2019.11

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    Language：English  

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  • Universal Gysin formulas for the universal Hall--Littlewood functions Reviewed

    Masaki Nakagawa, Hiroshi Naruse

    Contemporary Mathematics   708   201 - 244   2018.6

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    Language：English  

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  • Generalized (co)homology of the loop spaces of classical groups and the universal factorial Schur P- and Q-functions Reviewed

    Masaki Nakagawa, Hiroshi Naruse

    Advanced Studies in Pure Mathematics   71   337 - 417   2016.12

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    Language：English  

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  • The integral cohomology ring of E_8/T Reviewed

    Masaki Nakagawa

    Proceedings of Japan Academy, Series A Mathematical Sciences   86 ( 3 )   64 - 68   2010.3

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  • A description based on Schubert classes of cohomology of flag manifolds Reviewed

    Masaki Nakagawa

    Fundamenta Mathematicae   199 ( 3 )   273 - 293   2008.2

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    Language：English   Publishing type：Research paper (scientific journal)  

    We describe the integral cohomology rings of the flag manifolds of types Bn,Dn,G2 and F4 in terms of their Schubert classes. The main tool is the divided difference operators of Bernstein-Gelfand-Gelfand and Demazure. As an application, we compute the Chow rings of the corresponding complex algebraic groups, recovering thereby the results of R. Marlin. © Instytut Matematyczny PAN, 2008.

    DOI： 10.4064/fm199-3-5

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  • The Chern classes of the Hermitian symmetric space EVII Reviewed

    Masaki Nakagawa

    Far East Journal of Mathematical Sciences   20 ( 3 )   283 - 308   2006.3

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    Language：English  

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  • Cohomology operations in the space of loops on the exceptional Lie group E_6 Reviewed

    Masaki Nakagawa

    Journal of Mathematics of Kyoto University   44 ( 1 )   43 - 53   2004.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Kyoto University  

    DOI： 10.1215/kjm/1250283582

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  • The space of loops on the exceptional Lie group E_6 Reviewed

    Masaki Nakagawa

    Osaka Journal of Mathematics   40 ( 2 )   429 - 448   2003.6

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    Language：English  

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  • The mod 2 cohomology ring of the symmetric space EVI Reviewed

    Masaki Nakagawa

    Journal of Mathematics of Kyoto University   41 ( 3 )   535 - 556   2001.9

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Kyoto University  

    DOI： 10.1215/kjm/1250517617

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  • The integral cohomology ring of E_7/T Reviewed

    Masaki Nakagawa

    Journal of Mathematics of Kyoto University   41 ( 2 )   303 - 321   2001.6

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    Language：English  

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Research Projects

  • Equivariant Schubert calculus for p-compact groups

    Grant number：23K03092  2023.04 - 2026.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    中川 征樹, 西本 哲, 鳥居 猛, 奥山 真吾

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    Grant amount：\3510000 （ Direct expense: \2700000 、 Indirect expense：\810000 ）

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  • Research on topological models for combinatorial Hopf algebras

    2018.04 - 2021.03

    日本学術振興会  科学研究費補助金  基盤研究(C)

    Masaki Nakagawa, Hiroshi Naruse

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  • Development of learning materials with sensation by using virtual reality technology - in the case of three dimensional figures -

    Grant number：15K00921  2015.04 - 2019.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    Irie Takashi

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    Grant amount：\4420000 （ Direct expense: \3400000 、 Indirect expense：\1020000 ）

    The learning materials, which allow learners instinctive handling of three dimensional figures in the virtual reality space and offer them the characteristics of those figures through visual and kinematic sense, were developed by using a haptic device.
    (1) The material to experience the characteristics of basic three dimensional figures. (2) The material to experience the characteristics of regular polyhedrons and semi-regular polyhedrons. (3) The material to experience the transition of regular polyhedrons by truncation. In all materials, learners were able to contact the figures, hold them, move them, rotate them, and observe them from three directional view.

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  • Research on generalized cohomology of flag varieties and Schur functions and their variants

    2015.04 - 2018.03

    日本学術振興会  科学研究費補助金  基盤研究(C)

    Masaki Nakagawa

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  • Combinatorics of Schubert calculus and its application

    Grant number：25400041  2013.04 - 2016.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    NARUSE Hiroshi, IKEDA Takeshi, NAKAGAWA Masaki, ISHIKAWA Masao, HAGIWARA Manabu

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    Grant amount：\3770000 （ Direct expense: \2900000 、 Indirect expense：\870000 ）

    We defined good polynomial representative of torus equivariant Schubert class in K-theory of flag varieties of the classical groups. We also give combinatorial formula for them. As an application of equivariant Schubert calculus we give a proof of the hook formula, which gives the number of standard tableaux on a given shape of partition. We also give a generalization of the hook formula and its equivariant K-theory version. By alanogy with this formula we get a solution to the Casselman's problem related to the representation of p-adic algebraic groups using some techinques of Schubert calculus.

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  • Research on the loop spaces on Lie groups by combinatorial methods

    2012.04 - 2015.03

    日本学術振興会  科学研究費補助金  基盤研究(C)

    Masaki Nakagawa

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  • Morava K-theory of the exceptional Lie group and flag manifold

    Grant number：24540102  2012.04 - 2015.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    NISHIMOTO Tetsu, MIMURA Mamoru, NAKAGAWA Masaki

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    Grant amount：\2080000 （ Direct expense: \1600000 、 Indirect expense：\480000 ）

    In order to know the property of the fibre bundle, there is a way to calculate the characteristic classes. The most important fibre bundle is the universal bundle, and to determine its characteristic classes is equivalent to calculate the cohomology of the classifying space of the structure group. The spectral sequence is the tool to calculate the cohomology of the classifying space. This time, I calulated the E_2-term of the spectral sequence convergence to the mod 3 cohomology of the classifying spaces of the exceptional Lie groups E_7 and E_8. Moreover, I calculated the invariant ring of the Weyl group of E_7 which acts on the mod 3 cohomology of the classifying space of the maximal torus.

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  • Schubert calculus on flag varieties and its application

    Grant number：21540104  2009.04 - 2012.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    NAKAGAWA Masaki, MIMURA Mamoru, NARUSE Hiroshi, IKEDA Takeshi, NISHIMOTO Tetsu, KAJI Shizuo

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    Authorship：Principal investigator  Grant type：Competitive

    (1) We determined the ring structure of the integral cohomology ring of the flag manifold E_8/T, where E_8 denotes the compact simply-connected simple exceptional Lie group of rank 8 and T its maximal torus. We also identified the Schubert classes which generate this ring by means of the divided difference operators. Using this result, we were able to determine the Chow ring of the corresponding complex algebraic group E_8.
    (2) Using the localization technique and the GKM description of the torus equivariant cohomology rings of homogeneous spaces, we computed the torus equivariant cohomology ring of the flag variety G_2/B and the complex quadric Q_n explicitly, where G_2 denotes the complex Lie group of type G_2 and B a Borel subgroup.
    (3) Extending the result due to Kono-Kozima, we showed that the Pontrjagin ring of the based loop space of the infinite symplectic group Sp(resp. infinite orthogonal group SO) is isomorphic to the ring of Schur P-(resp. Q) functions

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  • Schubert geometry and special polynomials

    Grant number：20540053  2008 - 2010

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    IKEDA Takeshi, NARUSE Hiroshi, OHMOTO Toru, NAKAGAWA Masaki

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    Grant amount：\4550000 （ Direct expense: \3500000 、 Indirect expense：\1050000 ）

    For the flag variety of classical Lie groups, we introduced special polynomials representing the Schubert classes in torus equivariant cohomology ring. We established some fundamental properties for these polynomials. In order to extend this result to torus equivariant K-theory, we introduced special family of polynomials (K-theoretic Q-and P-functions) representing the Schubert classes in the torus equivariant K-theory of classical Grassmannian varieties. We also developed combinatorics of these polynomials. In particular, we discussed a relationship to excited Young diagrams and shifted set-valued tableaux. We introduced a Robinson-Schensted type algorithm for these tableaux. As an application of this algorithm, we proved Pieri type formulas for the K-theoretic Q-functions.

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  • On the characteristic classes and The Chow ring of the exceptional Lie groups

    Grant number：20540099  2008 - 2010

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    NISHIMOTO Tetsu, MIMURA Mamoru, NAKAGAWA Masaki

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    Grant amount：\3380000 （ Direct expense: \2600000 、 Indirect expense：\780000 ）

    In order to determine the cohomology of the classifying space of the exceptional Lie group, the action of the cohomology operation and the characteristic classes induced by the representation, we made some programs using some computer algebra system. We compute the cohomology of the classifying space of some exceptional Lie groups applying the programs.

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  • Invariants of the Weyl groups of exceptional Lie groups and their applications

    Grant number：18540106  2006.04 - 2009.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    Masaki Nakagawa

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    Grant type：Competitive

    ワイル群の不変量を用いたリー群の等質空間のコホモロジーの表示をもとに, 旗多様体, 対称空間, リー群上のループ空間などの位相幾何学的側面を研究する.

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  • Differential geometry of curves and surfaces (1) （2020academic year） Fourth semester  - 月5,月6

  • Differential geometry of curves and surfaces (2) （2020academic year） Fourth semester  - 月7,月8

  • Euclidean Geometry I (1) （2020academic year） 1st semester  - 木1,木2

  • Euclidean Geometry I (2) （2020academic year） Second semester  - 木1,木2

  • Introduction to Calculus （2020academic year） Third semester  - 木3,木4

  • Math for math teachers （2020academic year） Summer concentration  - その他

  • Seminar in Teaching Profession Practice (Secondary school A) （2020academic year） 1st-4th semester  - 水7,水8

  • Seminar in Teaching Profession Practice (Elementary school) （2020academic year） 1st-4th semester  - 水7,水8

  • Seminar in Teaching Profession Practice (Elementary school) （2020academic year） 1st-4th semester  - 水7,水8

  • Seminar in Teaching Profession Practice (Elementary school) （2020academic year） 1st-4th semester  - 水7,水8

  • Seminar in Teaching Profession Practice (Elementary school) （2020academic year） 1st-4th semester  - 水7,水8

  • Special Studies in Educational Science(Mathematics IC): Seminar （2020academic year） 1st semester  - 木5,木6

  • Special Studies in Educational Science(Mathematics IIC): Seminar （2020academic year） Second semester  - 木5,木6

  • Special Studies in Educational Science(Geometry IA) （2020academic year） 1st semester  - 火5,火6

  • Special Studies in Educational Science(Geometry IB) （2020academic year） Second semester  - 火5,火6

  • Special Studies in Educational Science(Geometry IIA) （2020academic year） Third semester  - 火3,火4

  • Special Studies in Educational Science(Geometry IIB) （2020academic year） Fourth semester  - 火3,火4

  • Project Research in Educational Science （2020academic year） 1st-4th semester  - その他

  • Elementary Mathematics (GeometryⅠ) （2020academic year） Third semester  - 金1,金2

  • Elementary Mathematics (GeometryⅡ) （2020academic year） Fourth semester  - 金1,金2

  • Elementary Geometry (1) （2020academic year） Third semester  - 金1,金2

  • Elementary Geometry (2) （2020academic year） Fourth semester  - 金1,金2

  • Introduction to Linear Algebra （2020academic year） Fourth semester  - 木3,木4

  • Set Theory and General Topology （2020academic year） 1st and 2nd semester  - 木7,木8

  • Set Theory and General Topology (1) （2020academic year） 1st semester  - 木7,木8

  • Set Theory and General Topology (2) （2020academic year） Second semester  - 木7,木8

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