Publications

1. Counting Commensurability Classes of Codimension One Subspaces (joint w. B. Linowitz)
   (in preparation)
2. Constructing Geometrically Equivalent Hyperbolic Orbifolds (joint w. D.B. McReynolds and M. Stover)
   (2015) arXiv Preprint
3. Systolic Surfaces of Arithmetic Hyperbolic 3-Manifolds (joint w. B. Linowitz)
   To appear in In the Tradition of Ahlfors-Bers, VII
   (2015) arXiv Preprint
4. The length spectra of arithmetic hyperbolic 3-manifolds and their totally geodesic surfaces
   (joint w. B. Linowitz and P. Pollack)
   (2015) New York J. Math Volume 21, 955-972.
   (2015) arXiv Preprint
5. Totally Geodesic Spectra of Quaternionic Hyperbolic Orbifolds
   (2015) arXiv Preprint
6. On the isospectral orbifold-manifold problem for nonpositively curved locally symmetric spaces
   (joint w. B. Linowitz)
   (2015) arXiv Preprint
7. Totally Geodesic Spectra of Arithmetic Hyperbolic Spaces
   (2014) arXiv Preprint
8. Division Algebras With Infinite Genus
   (2014) Bull. Lond. Math. Soc. 46 no. 3, 463-468.
   (2013) arXiv Preprint
   
9. On The Totally Geodesic Commensurability Spectrum of Arithmetic Locally Symmetric Spaces
   (2013) PhD Thesis. University of Michigan.

Interests

I work with arithmetic groups and quadratic forms, a fascinating area of mathematics that lies in the intersection of differential geometry and number theory. As such, my interests span a wide collection of areas including spectral geometry, geometric group theory, Lie theory, algebraic number theory, and class field theory. My thesis advisor was Matthew Stover.

Videos