Alden Waters (Bernoulli Institute)
Geometric and obstacle scattering at low energy.
We consider the problem of obstacle scattering for the Helmholtz equation with the p-form Laplace Beltrami operator. On manifolds which are asymptotically Euclidean we show resolvent expansions, and expansions for the scattering matrix. The key idea is the use of plane waves. We also give a cohomological interpretation of the scattered waves allowing us to identify geometric structures from afar. Joint work with F. Hanisch and A. Waters