Kings College, London

E B Davies has worked on the spectral analysis of self-adjoint Schrödinger operators for over twenty years, and is the author of two monographs in this general area. In the last four years he has turned his interests to the non-self-adjoint theory, which is far less well understood. He has obtained some of the first bounds on the locations of complex eigenvalues. These are important for reducing the work involved in trying to locate them numerically. He has proved that the larger eigenvalues of many non-self-adjoint differential operators are highly unstable. As a result any algorithm used to compute them is bound to run into difficulties. He has also become one of the experts in the subject of pseudo-spectral theory, which raises a lot of new perspectives in the field and leads to new questions. Several of these papers have a strong computational side. The non-self-adjoint theory has very close connections with the theory of resonances via the theory of complex scaling and exterior complex scaling, and he has obtained new results in this area in collaboration with A Aslanyan and A Abramov.