Details of the Researcher

PHOTO

Takeru Asaka
Section
Graduate School of Information Sciences
Job title

Research History 4

  • 2026/04 - Present
    東北大学大学院情報科学研究科　特任研究員

  • 2025/04 - 2026/03
    Tohoku University

  • 2024/03 - 2025/03
    Tohoku University

  • 2023/04 - 2024/03
    The University of Tokyo

Education 4

  • 東京大学大学院　数理科学研究科　数理科学専攻 博士課程

    2018/04 - 2023/03

  • 東京大学大学院　数理科学研究科　数理科学専攻 修士課程

    2016/04 - 2018/03

  • The University of Tokyo　Faculty of Science　Department of Mathematics

    2014/04 - 2016/03

  • The University of Tokyo

    2012/04 - 2014/03

Research Interests 6

  • function theory

  • complex analysis

  • quasiconformal map

  • earthquake theorem

  • cluster algebra

  • Teichmüller theory

Research Areas 1

  • Natural sciences / Geometry / low-dimensional topology

Papers 2

  1. The Fenchel–Nielsen twist in terms of the cross ratio coordinates Peer-reviewed

    Takeru Asaka

    Tsukuba Journal of mathematics　48　(2)　249-260　2024/12

  2. Earthquake Theorem for Cluster Algebras of Finite Type Peer-reviewed

    Takeru Asaka, Tsukasa Ishibashi, Shunsuke Kano

    International Mathematics Research Notices　2024　(8)　7129-7159　2024/02/23

    Publisher: Oxford University Press (OUP)

    DOI： 10.1093/imrn/rnae027 　

    ISSN： 1073-7928

    eISSN： 1687-0247

    More details Close

    Abstract We introduce a cluster algebraic generalization of Thurston’s earthquake map for the cluster algebras of finite type, which we call the cluster earthquake map. It is defined by gluing exponential maps, which is modeled after the earthquakes along ideal arcs. We prove an analogue of the earthquake theorem, which states that the cluster earthquake map gives a homeomorphism between the spaces of $\mathbb {R}^{\textrm {trop } }$- and $\mathbb {R}_{>0}$-valued points of the cluster $\mathcal {X}$-variety. For those of type $A_{n}$ and $D_{n}$, the cluster earthquake map indeed recovers the earthquake maps for marked disks and once-punctured marked disks, respectively. Moreover, we investigate certain asymptotic behaviors of the cluster earthquake map, which give rise to “continuous deformations” of the Fock–Goncharov fan.

Presentations 16

  1. 乱流ネットワーク Invited

    CREST「決定論的支配方程式による非線形・散逸・偶然性の動力学」因果解析班ミーティング　2025/12

  2. Earthquake theorem for cluster algebras of finite type

    30th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (ICFIDCAA 2024)　2024/08

  3. 地震定理とクラスター代数 Invited

    第64回 東北複素解析セミナー　2023/12

  4. Earthquake theorem and Cluster algebras Invited

    リーマン面に関連する位相幾何学　2023/08

  5. Some calculations about earthquake maps in the cross ratio coordinates Invited

    Advances in Cluster Algebras 2023　2023/03

  6. Earthquake theorem and Cluster algebras Invited

    リーマン面・不連続群論　2023/02

  7. Some calculations of an earthquake map in the cross ratio coordinates and the earthquake theorem of cluster algebras of finite type Invited

    トポロジー火曜セミナー　2023/02

  8. 地震定理とクラスター代数 Invited

    大阪大学数学教室セミナー　2022/12

  9. Earthquake theorem for cluster algebras of finite type

    浅香猛, 石橋典, 狩野隼輔

    日本数学会　2022/09

  10. Earthquake theorem for cluster algebras of finite type

    第56回函数論サマーセミナー　2022/09

  11. Earthquake theorem and cluster algebras Invited

    数理物理セミナー　2022/06

  12. Earthquake maps and cluster algebras

    浅香猛, 石橋典, 狩野隼輔

    日本数学会　2022/03

  13. クラスター代数と地震変形 Invited

    東北大学幾何セミナー　2022/02

  14. Earthquake theorem of cluster algebras of fintie type

    The 17th East Asian Conference on Geometric Topology　2022/01

  15. Earthquake maps of a once-punctured torus Invited

    早稲田双曲幾何幾何学的群論セミナー　2018/04

  16. Earthquake maps of a once-punctured torus Invited

    東京工業大学理学院数学系セミナー　2018/04

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Research Projects 3

  1. 地震定理のクラスター代数への拡張

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業（若手研究）

    Institution: 東北大学

    2026/04 - 2031/03

  2. 地震定理のクラスター代数への拡張

    Offer Organization: 日本学術振興会

    System: 特別研究員奨励費（特別研究員PD）

    Institution: 東北大学

    2026/04 - 2029/03

  3. 地震定理のクラスター代数への拡張

    Offer Organization: 住友財団 基礎科学研究助成

    2025/11 - 2027/11