David L. Webb

One cannot hear the shape of a drum

We use an extension of Sunadas theorem to construct a nonisometric pair of isospectral simply connected domains in the Euclidean plane, thus answering negatively Kacs question, can one hear the shape of a drum? In order to construct simply connected examples, we exploit the observation that an orbifold whose underlying space is a simply connected manifold with boundary need not be simply connected as an orbifold

The inaudible geometry of nilmanifolds.

SummaryWe show that isospectral deformations of compact Riemannian two-step nilmanifolds can be systematically detected by simple changes in the behavior of their geodesics, in spite of the fact that the length spectrum (which measures the lengths of all closed geodesics) remains constant.