What can the Steklov spectrum of a convex polygon tell us about the polygon’s geometry? Using a spectral invariant developed by Krymski, Levitin, Parnovski, Polterovich, and Sher, we can determine much about the geometry for certain classes of convex polygons, including quadrilaterals and regular polygons. More generally, we give conditions under which it is possible to "hear the corners" of a convex drum from the Steklov spectrum.
This talk is based on joint work with Carolyn Gordon, Javier Moreno, Julie Rowlett, and Carlos Villegas Blas.