Carolyn Gordon

Carolyn Sue Gordon (born December 26, 1950 in Charleston , West Virginia ) is an American mathematician who deals with differential geometry . She is particularly known for contributions to inverse spectral theory.

Scientific career

Gordon studied mathematics at Purdue University and received his doctorate in 1979 from Washington University under Edward Nathan Wilson on isometric groups of homogeneous manifolds. She then was a Lady Davis Fellow at the Technion in Haifa , was at Lehigh University and Washington University, before going to Dartmouth College in 1992 , where she is Professor of Mathematics.

From 2003 to 2005 she was President of the Association for Women in Mathematics .

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Gordon dealt with Riemannian geometry , and there especially with spectral problems (that is to the eigenvalues, the spectrum of the Laplace operator on Riemannian manifolds ), with the geometry of Lie groups and symmetric spaces and Kähler- and symplectic structures on Manifolds.

She became known when she and Scott Wolpert and David Webb gave an example of two simply connected two-dimensional manifolds that have the same sound spectrum (which corresponds mathematically to the spectrum of the Laplace operator on these surfaces), but different shapes (isospectal manifolds). With this they answered a famous question from Mark Kac from 1966 in the negative, whether one could hear the shape of a drum (Can one hear the shape of a drum?). It was already known that this was not possible in more than two dimensions, but the question in two dimensions (the actual aim of Kac's question) was open. They used a construction by Toshikazu Sunada .

Isospectral areas according to Gordon, Scott, Wolpert

Gordon later expanded the examples of isospectral manifolds for example in hyperbolic space - for example by specifying convex planar hyperbolic polygons - or by specifying isospectral convex bodies (their first example was not convex) in Euclidean space . She also found closed isospectral manifolds that are locally non- isometric .

She is co-editor of the Journal of Geometric Analysis.

Awards

In 1990 she received a Centennial Fellowship from the American Mathematical Society (AMS).
Together with David Webb, she received the Chauvenet Prize of the Mathematical Association of America (MAA) for You can't hear the shape of a drum .
In 1999 she was invited speaker at the joint meeting of the AMS and the MAA.
In 2010 she was a Noether Lecturer .
She is a Fellow of the American Mathematical Society.

Web links

Individual evidence

↑ Gordon, Webb, Wolpert One cannot hear the shape of a drum , Bulletin AMS, Volume 27, 1992, pp. 134-138 ( Online ), Isospectral plane domains and surfaces via Riemannian orbifolds , Inventiones Mathematicae, Volume 110, 1992, p 1-22
↑ More precisely, a distinction is made between Dirichlet and Neumann boundary conditions for bounded manifolds, whereby Dirichlet boundary conditions are meant in the question of the sound spectrum (the function disappears on the boundary), Gordon proved this, however, also for Neumann boundary conditions (first derivative disappears on the boundary ). Different forms are formulated mathematically as the question of whether they are isometric.
↑ Kac attributes the problem to Salomon Bochner , but made it popular in his essay. The approach also goes back to the work of Hermann Weyl at the beginning of the 20th century, who showed that the volume is determined from the spectrum.
↑ John Milnor first pointed out in 1964 (Proc. Nat. Acad. Sci., Volume 51, 542) that two isospectral tori in 16 dimensions could be constructed from Ernst Witt's theorem . Other examples came from Peter Buser, Marie-France Vignéras , Robert Brooks, Gordon himself and others.
↑ Further examples in two dimensions are given by Buser, John Conway, Doyle, Semmler .
↑ Isospectral closed Riemannian manifolds Which are not locally isometric , part 2, Contemporary Mathematics, vol 173, 1994, pp 121-131
↑ American Scientist, Volume 84, January / February 1996, pp. 46-55

personal data
SURNAME	Gordon, Carolyn
ALTERNATIVE NAMES	Gordon, Carolyn Sue; Gordon, Carolyn S.
BRIEF DESCRIPTION	American mathematician
DATE OF BIRTH	December 26, 1950
PLACE OF BIRTH	Charleston, West Virginia

[1] Gordon, Webb, Wolpert One cannot hear the shape of a drum , Bulletin AMS, Volume 27, 1992, pp. 134-138 ( Online ), Isospectral plane domains and surfaces via Riemannian orbifolds , Inventiones Mathematicae, Volume 110, 1992, p 1-22

[2] More precisely, a distinction is made between Dirichlet and Neumann boundary conditions for bounded manifolds, whereby Dirichlet boundary conditions are meant in the question of the sound spectrum (the function disappears on the boundary), Gordon proved this, however, also for Neumann boundary conditions (first derivative disappears on the boundary ). Different forms are formulated mathematically as the question of whether they are isometric.

[3] Kac attributes the problem to Salomon Bochner , but made it popular in his essay. The approach also goes back to the work of Hermann Weyl at the beginning of the 20th century, who showed that the volume is determined from the spectrum.

[4] John Milnor first pointed out in 1964 (Proc. Nat. Acad. Sci., Volume 51, 542) that two isospectral tori in 16 dimensions could be constructed from Ernst Witt's theorem . Other examples came from Peter Buser, Marie-France Vignéras , Robert Brooks, Gordon himself and others.

[5] Further examples in two dimensions are given by Buser, John Conway, Doyle, Semmler .

[6] Isospectral closed Riemannian manifolds Which are not locally isometric , part 2, Contemporary Mathematics, vol 173, 1994, pp 121-131

[7] American Scientist, Volume 84, January / February 1996, pp. 46-55