The Second Dirichlet Eigenvalue is Simple on Every Non-equilateral Triangle, Part II: Nearly Equilateral Triangles
Ryoki Endo, Xuefeng Liu
Accepted in Numerische Mathematik
Ryoki Endo
I received my Ph.D. in Science from Niigata University in March 2026. My research focuses on computer-assisted proofs with verified numerical computation for shape optimization problems and inverse spectral problems involving eigenvalues of differential operators.
Contact
Keywords
Degrees
Ph.D. in Science, Niigata University
M.Sc. in Science, Niigata University
Published Articles
The second Dirichlet eigenvalue is simple on every non-equilateral triangle, Part I: Nearly degenerate triangles
Ryoki Endo, Xuefeng Liu
Journal of Differential Equations 447, 113629
Stable Computation of Laplacian Eigenfunctions Corresponding to Clustered Eigenvalues
Ryoki Endo, Xuefeng Liu
Applications of Mathematics 70, 595–609
Shape optimization for the Laplacian eigenvalue over triangles and its application to interpolation error analysis
Ryoki Endo, Xuefeng Liu
Journal of Differential Equations 376, 750–772
Awards
ICNS2024 Student Presentation Award (Oral)
新潟大学 学生表彰
International Workshop on Reliable Computing and Computer-Assisted Proofs (ReCAP 2022) Student Presentation Award
Talks in Japanese
領域のスペクトル幾何学における計算機援用証明の現状と展望
Speaker(s): 遠藤凌輝
応用数学フレッシュマンセミナー2025
2025-11-08
Hadamard微分の厳密計算による固有値の単純性の解析
Speaker(s): 遠藤 凌輝, 劉 雪峰
日本応用数理学会2025年度年会
2025-09-02
三角形における Dirichlet 第 2 固有値の単純性について
Speaker(s): 遠藤凌輝, 劉雪峰
第4回 数理解析若手交流会
2024-12-21
Laplace作用素の近接固有値に対する単純性の厳密評価
2024年度 応用数学合同研究集会
2024-12-07
固有値が重複する領域の近傍における固有関数の安定計算法
Speaker(s): 遠藤凌輝, 劉雪峰
日本応用数理学会第20回研究部会連合発表会
2024-03-04
微分作用素の固有値に関する形状微分公式の精度保証付き数値計算と多角形領域の幾何
Speaker(s): 遠藤凌輝
Shape Seminar
2024-02-05 · 招待有り
クラスターを成す Laplace 作用素の固有値に対する形状微分の厳密計算法
Speaker(s): 遠藤凌輝, 劉雪峰
日本数学会 2023 年度秋季総合分科会
2023-09-23
ラプラシアンの重複固有値に関する形状微分公式と多角形領域の幾何
Speaker(s): 遠藤凌輝, 劉雪峰
日本応用数理学会第19回研究部会連合発表会
2023-03
三角形における Dirichlet 第 2 固有値の単純性について
Speaker(s): 遠藤 凌輝, 劉 雪峰
第4回 数理解析若手交流会
2022-12-21
三角形領域におけるラプラス作用素の固有値問題と形状微分公式の厳密評価
Speaker(s): 遠藤凌輝, 劉雪峰
日本応用数理学会2022年度年会
2022-09
Talks in English
Computer-assisted proof of the simplicity of the second Dirichlet eigenvalue for non-equilateral triangles
Speaker(s): Ryoki Endo, Xuefeng Liu
20th International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations (SCAN 2025)
2025-09-23
Computer-assisted verification of the simplicity of the second Dirichlet eigenvalue for non-equilateral triangles
Speaker(s): Ryoki Endo, Xuefeng Liu
Numerical methods for spectral problems: theory and applications 2025
2025-08-27
Computer-assisted proof of the simplicity of the second Laplacian eigenvalue for non-equilateral triangles
Speaker(s): Ryoki Endo, Xuefeng Liu
EASIAM2025 Manila
2025-07-02
Recent Advances in the Spectral Geometry of Domains and Approaches with Computer-Assisted Proofs
Speaker(s): Ryoki Endo
RIKEN iTHEMS Math Seminar
2024-12-12
Verified computation method for difference quotients of Laplacian eigenvalues
Speaker(s): Ryoki Endo, Xuefeng Liu
The 5th International Congress on Natural Sciences with Sisterhood Universities
2024-09-27
Verified computation method for difference quotients of Laplacian eigenvalues
Speaker(s): Ryoki Endo, Xuefeng Liu
Numerical methods for spectral problems: theory and applications 2024
2024-08-07
On the Simplicity of the Second Dirichlet Eigenvalue on Non-Equilateral Triangles
Speaker(s): Ryoki Endo
Symmetry-breaking of optimal shapes
2024-07-20
Verified computation for shape derivative of the Laplacian eigenvalues
Speaker(s): Ryoki Endo
Numerical methods for spectral problems: theory and applications 2023
2023-08-30
Verified computation for shape derivative of the Laplacian eigenvalues
Speaker(s): Ryoki Endo, Xuefeng Liu
ICIAM 2023 Tokyo Minisymposium: Verified Numerical Computations and Applications
2023-08-22
Guaranteed estimation of Hadamard shape derivative for clustered eigenvalues
Speaker(s): Ryoki Endo, Xuefeng Liu
Numerical Analysis Symposium 2023
2023-07-13
Academic Societies
The Mathematical Society of Japan
The Japan Society for Industrial and Applied Mathematics
Grants
Verified computation of Hadamard variations for eigenvalues and applications to spectral geometry
日本学術振興会 科学研究費助成事業 特別研究員奨励費 / JSPS Grant-in-Aid for JSPS Fellows
2024.04 – 2027.03