Carolyn S. Gordon
- Mathematical Association of America Chauvenet Prize
- Noether Lecture
- Fellow of the American Mathematical Society
- Fellow of American Association for the Advancement of Science
- Fellow of Association for Women in Mathematics
- President of the Association for Women in Mathematics
Carolyn S. Gordon (born 1950)[1] 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 Washington University in St. Louis.
Career
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/01/Isospectral_drums.svg/333px-Isospectral_drums.svg.png)
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 (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 convex isospectral domains in the hyperbolic plane[2] and in Euclidean space.[3]
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.[4]
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.[3][5]
Selected awards and honors
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 1990 she was awarded an AMS Centennial Fellowship by the American Mathematical Society for outstanding early career research. In 1999 Gordon presented an AMS-MAA joint invited address. In 2010 she was selected as a Noether Lecturer.[6] In 2012 she became a fellow of the American Mathematical Society[7] and of the American Association for the Advancement of Science.[8] She was also an AMS Council member at large from 2005 to 2007.[9] In 2017 she was selected as a fellow of the Association for Women in Mathematics in the inaugural class.[10] Gordon was featured in the Women's History Month tribute in the March 2018 edition of the AMS Notices.[11]
Selected articles
- Gordon, Carolyn (2001), "Isospectral Deformations of Metrics on Spheres", Inventiones Mathematicae, 145 (2): 317–331, arXiv:math/0005156, Bibcode:2001InMat.145..317G, doi:10.1007/s002220100150, S2CID 14078869
- Gordon, Carolyn; Webb, David (1996), "You can't hear the shape of a drum", American Scientist, 84 (January–February): 46–55, Bibcode:1996AmSci..84...46G
- Gordon, Carolyn (1994), Isospectral Closed Riemannian Manifolds which are not Locally Isometric II, Contemporary Mathematics, vol. 173, American Mathematical Society, pp. 121–131, doi:10.1090/conm/173/01821, ISBN 9780821851852
- Gordon, Carolyn; Webb, David; Wolpert, Scott (1992), "Isospectral plane domains and surfaces via Riemannian orbifolds", Inventiones Mathematicae, 110: 1–22, Bibcode:1992InMat.110....1G, doi:10.1007/BF01231320, S2CID 122258115
- Gordon, Carolyn; Webb, David L.; Wolpert, Scott (1992), "One Cannot Hear the Shape of a Drum", Bulletin of the American Mathematical Society, 27: 134–138, arXiv:math/9207215, doi:10.1090/S0273-0979-1992-00289-6, S2CID 15950835
- Gordon, Carolyn; Wilson, Edward (1984), "Isospectral deformations of compact solvmanifolds", Journal of Differential Geometry, 19: 241–256, doi:10.4310/jdg/1214438431
Personal life
Gordon is married to David Webb. She cites raising her daughter, Annalisa, as her greatest joy in life.[11]
References
- ^ Birth year from ISNI authority control file, accessed 2018-11-27.
- ^ Gordon, Carolyn S.; Webb, David L. (1994). "Isospectral convex domains in the hyperbolic plane". Proceedings of the American Mathematical Society. 120 (3). American Mathematical Society (AMS): 981–983. doi:10.1090/s0002-9939-1994-1181165-0. ISSN 0002-9939. S2CID 122328508.
- ^ a b mathscinet
- ^ Gordon, Carolyn S.; Wilson, Edward N. (1997-01-01). "Continuous families of isospectral Riemannian metrics which are not locally isometric". Journal of Differential Geometry. 47 (3). International Press of Boston. arXiv:dg-ga/9702011. doi:10.4310/jdg/1214460548. ISSN 0022-040X. S2CID 17159822.
- ^ Gordon, Carolyn; Mao, Yiping (1995). "Geodesic Conjugacy in two-step nilmanifolds". arXiv:math/9503220.
- ^ "Carolyn Gordon Named 2010 Noether Lecturer". Association for Women in Mathematics. Retrieved 7 April 2019.
- ^ List of Fellows of the American Mathematical Society, retrieved 2013-01-19.
- ^ Elected fellows, AAAS, retrieved 2017-10-30.
- ^ "AMS Committees". American Mathematical Society. Retrieved 2023-03-29.
- ^ "AWM Fellows Program". awm-math.org/awards/awm-fellows/. Association for Women in Mathematics. Retrieved 9 January 2021.
- ^ a b "Notices of the AMS" (PDF). p. 265. Retrieved 10 September 2018.
External links
- Carolyn S. Gordon at the Mathematics Genealogy Project
- Noether Announcement in July/Aug 2009 AWM Newsletter
- Carolyn S. Gordon
- v
- t
- e
- 1925 G. A. Bliss
- 1929 T. H. Hildebrandt
- 1932 G. H. Hardy
- 1935 Dunham Jackson
- 1938 G. T. Whyburn
- 1941 Saunders Mac Lane
- 1944 R. H. Cameron
- 1947 Paul Halmos
- 1950 Mark Kac
- 1953 E. J. McShane
- 1956 Richard H. Bruck
- 1960 Cornelius Lanczos
- 1963 Philip J. Davis
- 1964 Leon Henkin
- 1965 Jack K. Hale and Joseph P. LaSalle
- 1967 Guido Weiss
- 1968 Mark Kac
- 1970 Shiing-Shen Chern
- 1971 Norman Levinson
- 1972 François Trèves
- 1973 Carl D. Olds
- 1974 Peter D. Lax
- 1975 Martin Davis and Reuben Hersh
- 1976 Lawrence Zalcman
- 1977 W. Gilbert Strang
- 1978 Shreeram S. Abhyankar
- 1979 Neil J. A. Sloane
- 1980 Heinz Bauer
- 1981 Kenneth I. Gross
- 1982 No award given.
- 1983 No award given.
- 1984 R. Arthur Knoebel
- 1985 Carl Pomerance
- 1986 George Miel
- 1987 James H. Wilkinson
- 1988 Stephen Smale
- 1989 Jacob Korevaar
- 1990 David Allen Hoffman
- 1991 W. B. Raymond Lickorish and Kenneth C. Millett
- 1992 Steven G. Krantz
- 1993 David H. Bailey, Jonathan M. Borwein and Peter B. Borwein
- 1994 Barry Mazur
- 1995 Donald G. Saari
- 1996 Joan Birman
- 1997 Tom Hawkins
- 1998 Alan Edelman and Eric Kostlan
- 1999 Michael I. Rosen
- 2000 Don Zagier
- 2001 Carolyn S. Gordon and David L. Webb
- 2002 Ellen Gethner, Stan Wagon, and Brian Wick
- 2003 Thomas C. Hales
- 2004 Edward B. Burger
- 2005 John Stillwell
- 2006 Florian Pfender & Günter M. Ziegler
- 2007 Andrew J. Simoson
- 2008 Andrew Granville
- 2009 Harold P. Boas
- 2010 Brian J. McCartin
- 2011 Bjorn Poonen
- 2012 Dennis DeTurck, Herman Gluck, Daniel Pomerleano & David Shea Vela-Vick
- 2013 Robert Ghrist
- 2014 Ravi Vakil
- 2015 Dana Mackenzie
- 2016 Susan H. Marshall & Donald R. Smith
- 2017 Mark Schilling
- 2018 Daniel J. Velleman
- 2019 Tom Leinster
- 2020 Vladimir Pozdnyakov & J. Michael Steele
- 2021 Travis Kowalski
- 2022 William Dunham, Ezra Brown & Matthew Crawford
- 2023 Kimmo Eriksson & Jonas Eliasson
- 2024 Jeffrey Whitmer