Lp-Bounds on Spectral Clusters Associated to Polygonal Domains

With Matt Blair and Austin Ford, we discuss results that look at $L^p$ bounds on eigenfunctions in domains in $R^2$ with conic singularities.  Using explicit oscillatory integrals and relying on the fundamental solution to the wave equation in geometric regions related to flat wave propagation and diffraction by the cone point, we can prove spectral cluster estimates equivalent to those in works on smooth Riemannian manifolds.