Michael Levitin (University of Reading)

Title: Sharp eigenvalue asymptotics for Steklov problem on curvilinear polygons
Abstract: I will discuss a work in progress (joint with Leonid Parnovski, Iosif Polterovich and David Sher) on Steklov (or Dirichlet-to-Neumann map) eigenvalue asymptotics for curvilinear polygonal domains in R^2. The results are unexpected, and the asymptotics depends on the arithmetic properties of the angles of the polygon. There are also connections to classical problems of hydrodynamics (the sloping beach problem and the sloshing problem) and to the Laplacian on quantum graphs.