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

Slides from 2009 AMS Special Session at SFSU, Geometry and Topology of Orbifolds

"The Stratified Structure of Spaces of Smooth Orbifold Mappings" presented by Victor W. Brunsden, Penn State Altoona
"Diameters of spherical 3-orbifolds" presented by William D. Dunbar, Bard College at Simon's Rock
"Cohomogeneity 3 Actions on the Sphere" presented by J. McGowan, Howard University
"Bounds on 2-orbifold diffeomorphism type" presented by Emily B. Proctor, Middlebury College
"Connections between singular spaces: leaf spaces of Riemannian manifolds and orbifolds" presented by Mary R. Sandoval, Trinity College
"Generalized twisted sectors and applications" presented by Christopher Seaton, Rhodes College
"What is an orbigraph and what does one\ sound like?" presented by Liz Stanhope, Lewis & Clark College
"Geodesics on weighted projective spaces" presented by Zuoqin Wang, Johns Hopkins University