Updated on 2024/10/07

写真a

 
SHIMIZU, Ryosuke
 
Affiliation
Faculty of Science and Engineering, Waseda Research Institute for Science and Engineering
Job title
Junior Researcher(Assistant Professor)
Mail Address
メールアドレス
Homepage URL
https://rshimizu-math.github.io/

Research Experience

  • 2023.10
    -
    Now

    Waseda University   Faculty of Science and Engineering   Junior Researcher (Assistant Professor)

  • 2023.04
    -
    Now

    Japan Society for the Promotion of Science   Research Fellowships for Young Scientists (PD)

  • 2022.10
    -
    2023.03

    Japan Society for the Promotion of Science   Research Fellowships for Young Scientists (PD: changed the category)

  • 2020.04
    -
    2022.09

    Japan Society for the Promotion of Science   Research Fellowships for Young Scientists (DC1)

Education Background

  • 2020.04
    -
    2022.09

    Kyoto University   Graduate School of Informatics   Doctoral Course  

  • 2018.04
    -
    2020.03

    Kyoto University   Graduate School of Informatics   Master's Course  

  • 2014.04
    -
    2018.03

    Kyoto University   Faculty of Science   Faculty of Science  

Professional Memberships

  • 2021.10
    -
    Now

    日本数学会

Research Areas

  • Basic analysis

Research Interests

  • Sierpinski carpet

  • Ahlfors regular conformal dimension

  • potential theory

  • Sobolev space

  • fractal

Awards

 

Papers

  • Construction of 𝑝-energy and associated energy measures on Sierpiński carpets

    Ryosuke Shimizu

    Transactions of the American Mathematical Society, 377 (2024), no. 2,     951 - 1032  2023.10  [Refereed]

    　View Summary

    <p>We establish the existence of a scaling limit of discrete -energies on the graphs approximating a generalized Sierpiński carpet for , where is the Ahlfors regular conformal dimension of the underlying generalized Sierpiński carpet. Furthermore, the function space defined as the collection of functions with finite -energies is shown to be a reflexive and separable Banach space that is dense in the set of continuous functions with respect to the supremum norm. In particular, recovers the canonical regular Dirichlet form constructed by Barlow and Bass [Ann. Inst. H. Poincaré Probab. Statist. 25 (1989), pp. 225–257] or Kusuoka and Zhou [Probab. Theory Related Fields 93 (1992), pp. 169–196]. We also provide -energy measures associated with the constructed -energy and investigate its basic properties like self-similarity and chain rule.</p>

    DOI

    Scopus

    4
    Citation
    (Scopus)

  • Parabolic index of an infinite graph and Ahlfors regular conformal dimension of a self-similar set

    Ryosuke Shimizu

    Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs     201 - 274  2021.01  [Refereed]

    DOI

Presentations

▼display all

Research Projects

  • Analysis on complicated spaces using geometry of path families

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2023.04
    -
    2026.03
     

    Ryosuke Shimizu

  • Relation between nonlinear potential theory and geometry

    Project Year :

    2020.04
    -
    2023.03
     

    Ryosuke Shimizu

Misc