Wave decay rates and resonances in dimension two Abstract. Resonances are generalizations of eigenvalues used in settings where some or all of the spectrum is continuous rather than discrete. An example of such a setting is a wave in the exterior … Read more

Harmonic coordinates and asymptotic decay conditions Abstract. In General Relativity, an "isolated system at a given instant of time "is modeled as an asymptotically Euclidean (AE) initial data set (M,g,K) where (M,g) is a Riemannian manifold, K is a symmetric … Read more

One-dimensional hydrogenic ions with screened nuclear Coulomb field Abstract. We study the spectrum of the Dirac Hamiltonian in one space dimension for a single electron in the electrostatic potential of a point nucleus, in the Born-Oppenheimer approximation where the  nucleus … Read more

Higher codimension area-minimizers: structure of singularities and uniqueness of tangent cones Abstract. The problem of determining the size and structure of the interior singular set of area-minimizing surfaces has been studied thoroughly in a number of different frameworks, with many … Read more