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.
Keywords
Eigenvalues of the LaplacianComputer-assisted proofsShape optimizationInverse problems (“hearing the shape of a drum”)Collapsing domainsEigenvalue gapsBerry phase
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 II: Nearly Equilateral TrianglesAccepted in Numerische Mathematik
- The second Dirichlet eigenvalue is simple on every non-equilateral triangle, Part I: Nearly degenerate trianglesJournal of Differential Equations 447, 113629
- Stable Computation of Laplacian Eigenfunctions Corresponding to Clustered EigenvaluesApplications of Mathematics 70, 595–609
- Shape optimization for the Laplacian eigenvalue over triangles and its application to interpolation error analysisJournal 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 triangles20th 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 trianglesNumerical 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 trianglesEASIAM2025 Manila, 2025-07-02
- Recent Advances in the Spectral Geometry of Domains and Approaches with Computer-Assisted ProofsRIKEN iTHEMS Math Seminar, 2024-12-12
- Verified computation method for difference quotients of Laplacian eigenvaluesThe 5th International Congress on Natural Sciences with Sisterhood Universities, 2024-09-27
- Verified computation method for difference quotients of Laplacian eigenvaluesNumerical methods for spectral problems: theory and applications 2024, 2024-08-07
- On the Simplicity of the Second Dirichlet Eigenvalue on Non-Equilateral TrianglesSymmetry-breaking of optimal shapes, 2024-07-20
- Verified computation for shape derivative of the Laplacian eigenvaluesNumerical methods for spectral problems: theory and applications 2023, 2023-08-30
- Verified computation for shape derivative of the Laplacian eigenvaluesICIAM 2023 Tokyo Minisymposium: Verified Numerical Computations and Applications, 2023-08-22
- Guaranteed estimation of Hadamard shape derivative for clustered eigenvaluesNumerical 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