Prof. Braxton Osting
University of Utah

Title: "Extremal Steklov Eigenvalues"

Abstract: The Steklov eigenproblem is an eigenvalue problem where the eigenfunction is harmonic and the spectral parameter appears in the boundary condition. The Steklov spectrum coincides with that of the Dirichlet-to-Neumann map and appears in many important applications, such as sloshing fluids, electromagnetism, and imaging (medical, geophysical, etc..). In this talk, I'll discuss several extremal Steklov eigenvalue problems. In particular, for fixed k, we'll consider maximizing the k-th Steklov eigenvalue over a class of surfaces. I'll show how the solution of this problem, together with recent results of Fraser and Schoen, can be used to compute free boundary minimal surfaces, i.e., surfaces contained in the ball that have (i) zero mean curvature and (ii) meet the boundary of the ball orthogonally. This talk is based on joint work with Chiu-Yen Kao and Edouard Oudet.

Bio: Braxton Osting is an Associate Professor in the Department of Mathematics at the University of Utah. He received a B.S. from the University of Washington and a Ph.D. in Applied Mathematics from Columbia University. Before moving to Utah, he was an NSF Postdoctoral Fellow at the University of California, Los Angeles. He has broad interests in analytical and computational methods for problems in applied mathematics, especially in partial differential equations, optimization and control, graph theory, and machine learning.

Host: Amir Sagiv