15:00: John Toth (McGill University): Nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces
We prove sharp upper and lower bounds for the nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces with boundary. The argument involves frequency function methods for harmonic functions in the interior of the surface as well as the construction of exponentially accurate approximations for the Steklov eigenfunctions near the boundary. This is joint work with Iosif Polterovich and David Sher.
16:30: Jared Wunsch (Northwestern University): Diffractive propagation on conic manifolds
Solutions to the wave equation on manifolds with conic singularities are affected by diffraction at the cone points. I will discuss some recent results about wave propagation on conic manifolds including local energy decay rates, Strichartz estimates, and a trace formula for the wave group.