American Institute of Mathematics, San Jose, California
Oscar Bruno, Michael Levitin, Nilima Nigam, and Iosif Polterovich
Steklov eigenproblems (with the spectral parameter appearing in the boundary conditions) have been the subject of intense mathematical investigation over the past several years in a range of areas of mathematics. Recently, there has been a growing interest in this topic from the viewpoint of spectral geometry. Steklov problems arise in a number of important applications, notably, in hydrodynamics (through the Steklov type sloshing eigenvalue problem describing small oscillations of fluid in an open vessel), and in medical and geophysical imaging (via the link between the Steklov problem and the celebrated Dirichlet-to-Neumann map). Any progress made in the area during the workshop could therefore have a wide mathematical impact.
The main purpose of the workshop is to combine deep theoretical analysis with highly accurate and efficient numerical methods, in order to study various geometric features of the Steklov eigenvalues and eigenfunctions. The questions of interest are quite challenging because they are at the forefront of research in both numerical analysis and spectral geometry. These communities do not significantly overlap, and this workshop will provide a rare opportunity for researchers on both numerical and theoretical sides to get together, brainstorm, and share expertise across fields. Advanced analytic techniques would help creating "right" numerical methods, which in turn should improve the geometric and analytic intuition, and lead to discoveries of new phenomena.
We aim to make progress on the following four related topics:
The workshop schedule.
A report on the workshop activities.
A list of open problems.