SFU Mathematics of Computation, Application and Data ("MOCAD") Seminar: Xuefeng Liu

This talk introduces a newly developed computational method for rigorously evaluating the Hadamard derivative of Laplacian eigenvalues, which plays an important role in studying shape optimization problems. 

To evaluate the Hadamard derivative, this method employs state-of-the-art algorithms for eigenvalues and eigenfunctions via the finite element method (Liu'2013,2015; Liu-Vejchodsky'2022), effectively handling cases of repeated or closely spaced eigenvalues. 

We also present a computer-assisted proof for the optimization and simplicity of Laplacian eigenvalues over triangular domains (Endo-Liu'2023,2024), demonstrating the impact of these computational advancements in spectral geometry.