The Steklov Spectrum of Convex Euclidean Polygons

Explore the Steklov spectrum of convex Euclidean polygons in this hour-long seminar from the "Spectral Geometry in the clouds" series. Delve into upper bounds for Steklov eigenvalues normalized by perimeter in convex polygons. Investigate the inverse problem for the Steklov spectrum, examining how generic convex n-gons can be determined among all n-gons by their spectra. Learn about a key result demonstrating unique determination of certain convex n-gons with obtuse interior angles and incommensurable side lengths. Discover the powerful Steklov spectral invariants and new eigenvalue bounds used as main tools in addressing the inverse spectral problem. This talk presents joint work with Emily Dryden, Javier Moreno, Julie Rowlett, and Carlos Villegas Blas.