Chiu-Yen Kao (Claremont McKenna College)

Title: Geometric Optimization Involving Partial Differential Equations and Its Applications

Speaker: Professor Chiu-Yen Kao, Claremont McKenna College, Claremont, CA USA

Abstract: Optimal geometric design for energy functionals, which depends on solutions to partial differential equations, provides a vast number of interesting and challenging mathematical problems. One of the famous problems is that L. Rayleigh conjectured that the disk should minimize the fundamental frequency of vibration (the square root of the first Laplace-Dirichlet eigenvalue) among all shapes of equal area, more than a century ago. In this talk, we will share our recent findings related to geometric optimization for eigenvalue problems. Our approach involves the development of various computational methods to optimize Steklov eigenvalues and Laplace-Beltrami eigenvalues. Additionally, we explore applications of these methods.