Carolyn S. Gordon
Carolyn S. Gordon is an American mathematician who is the Benjamin Cheney Professor of Mathematics at Dartmouth College. She is most well known for giving a negative answer to the question "Can you hear the shape of a drum?" in her work with David Webb and Scott A. Wolpert. She is a Chauvenet Prize winner and a 2010 Noether Lecturer.
Early life and education
Gordon received her Bachelor of Science degree from Purdue University. She entered graduate studies at the Washington University in St. Louis, earning her Doctor of Philosophy in mathematics in 1979. Her doctoral advisor was Edward Nathan Wilson and her thesis was on isometry groups of homogeneous manifolds. She completed a postdoc at Technion – Israel Institute of Technology and held positions at Lehigh University and in the Arts and Sciences at Washington University in St. Louis.Career
Gordon is most well known for her work in isospectral geometry, for which hearing the shape of a drum is the prototypical example. In 1966 Mark Kac asked whether the shape of a drum could be determined by the sound it makes. John Milnor observed that a theorem due to Witt implied the existence of a pair of 16-dimensional tori that have the same spectrum but different shapes. However, the problem in two dimensions remained open until 1992, when Gordon, with coauthors Webb and Wolpert, constructed a pair of regions in the Euclidean plane that have different shapes but identical eigenvalues . In further work, Gordon and Webb produced convex isospectral domains in the hyperbolic plane and in Euclidean space.Gordon has written or coauthored over 30 articles on isospectral geometry including work on isospectral closed Riemannian manifolds with a common Riemannian covering. These isospectral Riemannian manifolds have the same local geometry but different topology. They can be found using the "Sunada method," due to Toshikazu Sunada. In 1993 she found isospectral Riemannian manifolds which are not locally isometric and, since that time, has worked with coauthors to produce a number of other such examples.
Gordon has also worked on projects concerning the homology class, length spectrum and geodesic flow on isospectral Riemannian manifolds.