School navigation

Mathematical Sciences

Liz Stanhope

Associate Professor of Mathematics

BoDine Hall

Specialty

Spectral geometry, Spectral graph theory, Quantitative biology education

Teaching

Please CLICK HERE to get to Prof. Stanhope’s website.

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 and Steklov spectral geometry of Riemannian orbifolds, as well as spectral graph theory. I also do discipline-based undergraduate research in quantitative biology education.

Publications and Preprints:  (* indicates undergraduate coauthors)

Richardson*, S.; Stanhope, E. You can hear the local orientability of an orbifold. to appear in Differential Geometry and its Applications.

Daly*, K.; Gavin*, C.; Montes de Oca*, G.; Ochoa*, D.; Stanhope, E.; Stewart*, S.  Orbigraphs: a graph-theoretic analog to Riemannian orbifolds. Involve 12 (2019), no. 5, 721–736.

Arias-Marco, T.; Dryden, E. B.; Gordon, C. S.; Hassannezhad, A.; Ray, A.; Stanhope, E. Spectral geometry of the Steklov problem on orbifolds. Int. Math. Res. Not. IMRN 2019, no. 1, 90–139. 

E. Stanhope, L. Ziegler, T. Haque, L. Le, M. Vinces, G. Davis, A. Zieffler, P. Brodfuehrer, M. Preest, J. Belitsky, C. Umbanhowar Jr., P. Overvoorde. Development of a Biological Science Quantitative Reasoning Exam (BioSQuaRE). CBE Life Sci. Educ., 16 (2017), no. 4.

Stanhope, E.; Uribe, A. The spectral function of a Riemannian orbifold. Ann. Global Anal. Geom. 40 (2011), no. 1, 47–65. 

Proctor, E.; Stanhope, E. Spectral and geometric bounds on 2-orbifold diffeomorphism type. Differential Geom. Appl. 28 (2010), no. 1, 12–18. 

Proctor, E.; Stanhope, E. An isospectral deformation on an infranil-orbifold. Canad. Math. Bull. 53 (2010), no. 4, 684–689.

“One cannot hear orbifold isotropy type,” Shams, N.; Stanhope, E.; Webb, D. L.  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, PhD Thesis, Dartmouth College. pdf | postscript