This three-year award will support U.S.-France cooperative research in mathematics and involves ten U.S. university-based investigators, including 5 recent doctorates, and an equal number of investigators in Grenoble, France. The American and French groups, consisting of participants from different institutions, will be led by Carolyn Gordon of Dartmouth College and Pierre Berard of the Institut Fourier, University of Grenoble. The focus of their research is inverse spectral problems in Riemannian geometry. They will study the extent to which eigenvalue spectrum of the Laplace operator on a Riemannian manifold determines the geometry of the manifold. This problem is frequently phrased as `Can one hear the shape of a drum.` General techniques for constructing manifolds with the same spectrum; questions of spectral rigidity; and relationships between the spectrum and the geometry of Riemannian manifolds will be addressed. The proposal brings together mathematicians with complementary abilities and mutual interests. The results of the project will have important applications in all fields of mathematics and for example, in signal processing and remote sensing.
