Geometric Scattering Theory

These lecture notes are intended as a non-technical overview of scattering theory. The point of view adopted throughout is that scattering theory provides a parameterization of the continuous spectrum of an elliptic operator on a complete manifold with uniform structure at infinity. The simple and fundamental case of the Laplacian or Euclidean space is described in the first two lectures to introduce the basic framework of scattering theory. In the next three lectures various results on Euclidean scattering, and the methods used to prove them, are outlined. In the last three lectures these ideas are extended to non-Euclidean settings. These lecture notes will be of interest to graduate students and researchers in the field of applied mathematics.

List of illustrations; Introduction; 1. Euclidean Laplacian; 2. Potential scattering on Rn; 3. Inverse scattering; 4. Trace formulae and scattering poles; 5. Obstacle scattering; 6. Scattering metrics; 7. Cylindrical ends; 8. Hyperbolic metrics.

These lecture notes provide a non-technical overview of scattering theory. The simple case of the Laplacian or Euclidean space is described in the first two lectures. Various results on Euclidean scattering are then outlined. In the last three lectures these ideas are extended to non-Euclidean settings.