Carolyn S. Gordon

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Carolyn S. Gordon is a mathematician and professor of mathematics at Dartmouth College since 1992. She received her Bachelor of Science degree from the Purdue University, then studied at the Washington University, 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 Washington University. In 1990 she was awarded an AMS Centennial Fellowship by the American Mathematical Society.[1]

This is the Gordon–Webb–Wolpert example of two flat surfaces with the same spectrum. Notice that both polygons have the same area and perimeter.

Gordon is most well known for her work in isospectral geometry which concerns hearing the shape of a drum. In 1966 Mark Kac asked whether the shape of a drum could be determined by the sound it makes (whether a Riemannian manifold is determined by the spectrum of its Laplace-Beltrami operator). 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 (see figure on right). In further work, Gordon and Webb produced isospectral domains in hyperbolic space and convex isospectral domains in the Euclidean plane.[2]

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. 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.[3]

Gordon has also worked on projects concerning the homology class, length spectrum (the collection of lengths of all closed geodesics, together with multiplicities) and geodesic flow on isospectral Riemannian manifolds.[4]

Awards and honors[edit]

In 2001 Gordon and Webb were awarded the Mathematical Association of America Chauvenet Prize for their 1996 American Scientist paper, "You can't hear the shape of a drum". In 1999 Gordon presented an AMS-MAA joint invited address. In 2010 she was selected as a Noether Lecturer.[5] In 2012 she became a fellow of the American Mathematical Society.[6]

Doctoral Students[edit]

He Ouyang Washington University 1991

Ruth Gornet Washington University 1993

Elizabeth Stanhope Dartmouth College 2002

Emily Proctor Dartmouth College 2003

Emily Dryden Dartmouth College 2004

Ian Adelstein Dartmouth College 2015 [7]

References[edit]

  1. ^ Press release of the AWM
  2. ^ mathscinet
  3. ^ mathscinet
  4. ^ mathscinet
  5. ^ Press release of the AWM
  6. ^ List of Fellows of the American Mathematical Society, retrieved 2013-01-19.
  7. ^ Carolyn S. Gordon at the Mathematics Genealogy Project

Selected articles[edit]

External links[edit]