GSTW02 — Geometry of eigenvalues

The study of the geometric properties of eigenvalues is closely linked to geometric analysis, applied mathematics and mathematical physics. A striking interplay with the theory of minimal surfaces and recently discovered connections to homogenisation theory have led to new sharp isoperimetric inequalities for Laplace and Steklov eigenvalues on Riemannian manifolds. The latest progress on Neumann and Robin eigenvalues, as well as emerging research on the spectra of other physically important operators, such as Dirac and curl, further highlight the expanding scope of the field and its applications. The workshop aims to bring together a diverse group of experts working on these and related topics. By fostering the exchange of ideas and methodologies, the meeting seeks to inspire innovative approaches to open problems and to advance the broader landscape of spectral geometry.