MANO Toshiyuki

写真a

Title

Professor

Researcher Number(JSPS Kakenhi)

60378594
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Current Affiliation Organization 【 display / non-display 】

  • Duty   University of the Ryukyus   Faculty of Science   Mathematical Sciences   Professor  

  • Concurrently   University of the Ryukyus   Graduate School of Engineering and Science   Mathematical Sciences   Professor  

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External Career 【 display / non-display 】

  • 2009.11
    -
    2012.07

    University of the Ryukyus, Faculty of Science, Research Associate  

  • 2012.08
    -
    2020.11

     

  • 2020.12
    　
    　

     

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Affiliated academic organizations 【 display / non-display 】

  • 1999.04
    -
    Now
     

    Mathematical Society of Japan 

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Research Interests 【 display / non-display 】

  • Differential equations of complex variables,Theory of special functions

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Research Areas 【 display / non-display 】

  • Natural Science / Mathematical analysis

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Published Papers 【 display / non-display 】

  • Flat Structure on the Space of Isomonodromic Deformations

    Mitsuo Kato, Toshiyuki Mano, Jiro Sekiguchi

    Symmetry, Integrability and Geometry: Methods and Applications ( SIGMA (Symmetry, Integrability and Geometry: Methods and Application) )  16   1 - 36   2020.11 [ Peer Review Accepted ]

    Type of publication: Research paper (scientific journal)

    　View Summary

    Flat structure was introduced by K. Saito and his collaborators at the end of 1970's. Independently the WDVV equation arose from the 2D topological field theory. B. Dubrovin unified these two notions as Frobenius manifold structure. In this paper, we study isomonodromic deformations of an Okubo system, which is a special kind of systems of linear differential equations. We show that the space of independent variables of such isomonodromic deformations can be equipped with a Saito structure (without a metric), which was introduced by C. Sabbah as a generalization of Frobenius manifold. As its consequence, we introduce flat basic invariants of well-generated finite complex reflection groups and give explicit descriptions of Saito structures (without metrics) obtained from algebraic solutions to the sixth Painlevé equation.

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  • Potential vector fields and isomonodromic tau functions in terms of flat coordinates

    Toshiyuki Mano

    "Complex Differential and Difference Equations" in the series De Gruyter Proceedings in Mathematics.     327 - 342   2019.11 [ Peer Review Accepted ]

    Type of publication: Research paper (scientific journal)

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  • Solutions to the extended WDVV equations and the Painleve VI equation

    M. Kato, T. Mano, J. Sekiguchi

    "Complex Differential and Difference Equations" in the series De Gruyter Proceedings in Mathematics     343 - 363   2019.11 [ Peer Review Accepted ]

    Type of publication: Research paper (scientific journal)

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  • Freeness of multi-reflection arrangements via primitive vector fields

    T. Hoge, T. Mano, G. Rohrle, C. Stump

    Advances in Mathematics ( Advances in Mathematics )  350   63 - 96   2019.07 [ Peer Review Accepted ]

    Type of publication: Research paper (scientific journal)

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  • Regular flat structure and generalized Okubo system

    H. Kawakami, T. Mano

    Communications in Mathematical Physics ( Communications in Mathematical Physics )  369 ( 2 ) 403 - 431   2019.07 [ Peer Review Accepted ]

    Type of publication: Research paper (scientific journal)

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Books 【 display / non-display 】

  • Introduction to Flat structure with Applications to Complex reflection groups and Painleve equations

    Toshiyuki Mano ( Part: Single Author )

    2022.12

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Presentations 【 display / non-display 】

  • On a geometric notion associated with linear differential equations of Okubo normal form

    Toshiyuki Mano

    Complex Differential and Difference Equations II  (Mathematical Research and Conference Center, Bedlewo)  2023.08  -  2023.09 

  • Flat structures on solutions to the sixth Painleve equation

    Toshiyuki Mano

    Web-seminar on Painleve Equations and related topics  2023.02  -  2023.02 

  • Period of primitive forms, the space of Okubo-Saito potentials and the sixth Painleve equation

    Toshiyuki Mano

    Painleve Equations: From Classical to Modern Analysis  (Institut de recherche mathematique avancee (IRMA), Strasbourg)  2022.10  -  2022.10 

  • Flat structure on the orbit space of a complex reflection group

    Toshiyuki Mano

    Silver Workshop: Complex Geometry and Non-Commutative Geometry  2019.02  -  2019.02 

  • Analytic representation of potential vector fields and isomonodromic tau-functions

    Toshiyuki Mano

    Complex differential and difference equations  2018.09  -  2018.09 

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