# Colloquium: Dr. Chiu-Yen Kao

UW-Milwaukee Department of Mathematical Sciences presents,

Dr. Chiu-Yen Kao;
Associate Professor of Mathematical Sciences
Claremont McKenna College

Friday, May 6, 2016
2:00pm in EMS E495

*Refreshments will be served at 1:30pm in EMS E424A*

Title:
Computational Methods for Extremal Steklov Problems

Description/Abstract:
We develop a computational method for extremal Steklov eigenvalue problems and apply it to study the problem of maximizing the p-th Steklov eigenvalue as a function of the domain with a volume constraint. In contrast to the optimal domains for several other extremal Dirichlet- and Neumann-Laplacian eigenvalue problems, computational results suggest that the optimal domains for this problem are very structured. We reach the conjecture that the domain maximizing the p-th Steklov eigenvalue is unique (up to dilations and rigid transformations), has p-fold symmetry, and an axis of symmetry. The p-th Steklov eigenvalue has multiplicity 2 if p is even and multiplicity 3 if p>=3 is odd.