This award supports Professor Thomas P. Branson and Palle Jorgensen of the University of Iowa and Peter Gilkey of the University of Oregon to collaborate in applied mathematics with three strong research groups in Germany and Denmark. Their partners are Gestur Olafsson, University of Gottingen, Reinhard Werner, University of Osnabruck, Bent Oersted, Odense University and Henrik Schlichtkrull, Danish Royal Veterinary and Agricultural University. Their collaboration is framed around six topics within the general area of "spectral theory." These problems are motivated in part by questions in mathematical physics and also in conformal geometry, and will be approached with methods from modern analysis and partial differential operators. This field is one of great activity in Europe, with many strong groups and a long tradition of research that offers diverse opportunities for U.S. participation. In this cooperative project, the U.S. participants offer technical power in the "hard analytic" and geometric aspects, while the European groups bring great strengths in invariance group methods. Spectral theory is the mathematical underpinning of all scientific work involving a spectrum, ranging from the theories of light and electromagnetism to chemistry. In mathematics, spectral theory is a major tool in work in several areas in geometry and analysis.
