Associate Professor of Mathematics
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