题目：Guaranteed Computation for Hadamard Derivatives of Eigenvalues and Its Applications

报告人：刘雪峰 教授，东京女子大学（日本）

时间：2025年7月14日（周一）16:00-17:00

地点：东区五教5206

摘要：We investigate the Hadamard shape derivative of eigenvalues from the perspective of rigorous computation. This study originated from our earlier work on interpolation error constants in the finite element method, developed over the past decade. Recently, we have established guaranteed computational methods for both simple and multiple eigenvalues. These rigorous techniques, which include the guaranteed computation of eigenvalues, eigenfunctions, and their shape derivatives, offer powerful tools for addressing open problems in spectral geometry. As a concrete application, we resolve the long-standing question of the simplicity of the second Dirichlet Laplacian eigenvalue on a triangular domain. Furthermore, with a newly proposed “difference quotient” computation algorithm, we developed a method for computing eigenfunctions associated with tightly clustered eigenvalues—a classically ill-posed problem. This method enables stable and reliable computation in such challenging scenarios.

This research is conducted in collaboration with JSPS DC researcher Mr. Ryoki Endo at Niigata University.

报告人简介：2003年毕业于中国科学技术大学，2009年在日本东京大学取得博士学位。先后在早稻田大学以及新潟大学工作，2023年任职东京女子大学教授。长期从事有限元计算方法的严格误差估计理论，及其在计算机辅助数学证明中的应用。2024年7月出版特征值问题的严格计算为主题的专著：Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems, Springer Singapore