中村 あかね (ナカムラ アカネ)

NAKAMURA Akane

写真a

出身大学院 【 表示 / 非表示

  •  
    -
    2015年03月

    東京大学  数理科学研究科  博士課程  修了

留学歴 【 表示 / 非表示

  • 2015年08月
    -
    2016年03月

    Sydney大学   Postdoctoral Research Associate

 

学位論文 【 表示 / 非表示

  • Autonomous limit of 4-dimensional Painlevé-type equations and degeneration of curves of genus two

    Akane Nakamura

      2015年03月

    学位論文(その他)   単著

論文 【 表示 / 非表示

  • Uniqueness of polarization for the autonomous 4-dimensional Painlevé-type systems

    Akane Nakamura, Eric Rains

    International Mathematics Research Notices ( Oxford Academic Journals )    2020年02月  [査読有り]

    単著

    DOI arXiv

  • The Painlevé divisors of the autonomous 4-dimensional Painlevé-type equations

    Akane Nakamura

        2020年  [査読有り]

    単著

  • Autonomous limit of 4-dimensional Painlevé-type equations and degeneration of curves of genus two

    Annales de l'Institut Fourier   69 ( 2 ) 845 - 893   2019年  [査読有り]

    単著

    DOI arXiv

  • Degeneration scheme of 4-dimensional Painlevé-type equations

    H. Kawakami, H. Sakai

    MSJ Memoir   37   25 - 111   2018年  [査読有り]

    共著

    Four 4-dimensional Painlev\'e-type equations are obtained by isomonodromic deformation of Fuchsian equations: they are the Garnier system in two variables, the Fuji-Suzuki system, the Sasano system, and the sixth matrix Painlev\'e system. Degenerating these four source equations, we systematically obtained other 4-dimensional Painlev\'e-type equations. If we only consider Painlev\'e-type equations whose associated linear equations are of unramified type, there are 22 types of 4-dimensional Painlev\'e-type equations: 9 of them are partial differential equations, 13 of them are ordinary differential equations. Some well-known equations such as Noumi-Yamada systems are included in this list. They are written as Hamiltonian systems, and their Hamiltonians are neatly written using Hamiltonians of the classical Painlev\'e equations.

    arXiv

  • Two aspects of the theta divisor associated with the autonomous Garnier system of type 9/2

    Akane Nakamura

    JMM 10, Representation Theory and Differential Equations     2017年  [査読有り]

    単著

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科研費(文科省・学振)獲得実績 【 表示 / 非表示

  • 高次元パンルヴェ型方程式の非線型・線型対応に関する研究

    若手研究

    研究期間:  2020年04月  -  2023年04月  代表者:  中村あかね