The Steklov Problem with Piecewise Smooth Boundary

This seminar talk from the "Spectral Geometry in the clouds" series features Jeff Galkowski from University College London discussing the Steklov problem with piecewise smooth boundary. Explore an approach based on scattering theory for studying the Steklov problem on domains with piecewise smooth, Lipschitz boundaries. Learn how this method can be applied to study eigenvalues and eigenfunctions of the Steklov problem on piecewise smooth, Lipschitz domains in dimension two, improving upon earlier work by Levitin–Parnovski–Polterovich–Sher. The presentation also indicates further developments needed to understand the problem in higher dimensions. The talk is based on joint work with M. Malagutti and R. Wang, presented on December 2, 2024, as part of the Centre de recherches mathématiques (CRM) seminar series.