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Mathematical Sciences

Liz Stanhope

Associate Professor of Mathematics

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BoDine Hall

Research

Fun research description:

  • My research interests lie in the subfield of differential geometry called spectral geometry. I ask, “If you can hear how an object vibrates, can you say anything about the shape of the object?”
  • In 1966 mathematician Mark Kac asked a now famous question, “Can you hear the shape of a drum?” His question was answered in 1991, check out this  American Math Society page  to learn more.  Movies of these isospectral drums vibrating can be found at this link.
  • An applet demonstrating the vibration of a circular drum can be found at this link.

Fun yet formal research description:

I study the (Laplace) spectral geometry of Riemannian orbifolds, and the topological properties of orbifolds which satisfy Ricci or sectional curvature bounds. I am also interested in spectral graph theory.

Publications and Preprints:  (* indicates undergraduate coauthors)

  • “Spectral and geometric bounds on 2-orbifold diffeomorphism type,” Emily Proctor, Elizabeth Stanhope. To appear in Differential Geometry and its Applications.  Preprint
  • “The normalized Laplace spectrum and weighted quotients of graphs,” Karsten Gimre*, Indra Shottland*, Elizabeth Stanhope. in preparation  Preprint
  • “An isospectral deformation of an orbifold quotient of a nilmanifold,” Emily Proctor, Elizabeth Stanhope.  To appear in Canadian Mathematical Bulletin.  Preprint
  • “One cannot hear orbifold isotropy type,” Naveed Shams, Elizabeth Stanhope, David L. Webb.  Arch. Math. (Basel) 87 (2006), no. 4, 375–384.  Preprint
  • “Spectral bounds on orbifold isotropy,” Elizabeth Stanhope. Annals of Global Analysis and Geometry 27 (2005), no. 4, 355–375.  Preprint
  • “Hearing orbifold topology,” Elizabeth Stanhope, Spring 2002, Ph.D. Thesis, Dartmouth College. pdf | postscript
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