Title: Spectral geometry of the Steklov problem
Abstract:
The Steklov problem is an elliptic eigenvalue problem with the spectral parameter in the boundary conditions. While this problem shares some common properties with its more well known Dirichlet and Neumann cousins, the Steklov eigenvalues and eigenfunctions have a number of distinctive geometric features. We will discuss some recent advances in the subject, particularly in the study of spectral asymptotics, spectral invariants, eigenvalue estimates, and nodal geometry. The talk is based on a joint survey article with A. Girouard.