Propagation of waves on domains with boundary
We are concerned with localization properties of solutions to hyperbolic PDEs, especially problems with a
geometric component: how do boundaries influence spreading and concentration of solutions.
Our first focus is on wave and Schrödinger equations on manifolds with boundary, but strong connections
exist with phase space localization for (clusters of) eigenfunctions, which are of independent interest.
Motivations come from nonlinear dispersive models (in physically relevant settings), properties of eigenfunctions
in quantum chaos, or harmonic analysis on manifolds.
