Mathematical 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.
Preprints and Works In Progress  Counting Commensurability Classes of Codimension One Subspaces (joint w. B. Linowitz)
(in preparation)
 Totally Geodesic Spectra of Quaternionic Hyperbolic Orbifolds
(2015) arXiv Preprint
Publications
 Constructing Geometrically Equivalent Hyperbolic Orbifolds (joint w. D.B. McReynolds and M. Stover)
(2017) Algebraic & Geometric Topology, Volume 17, no. 2, 831846.
(2015) arXiv Preprint
 On the isospectral orbifoldmanifold problem for nonpositively curved locally symmetric spaces
(joint w. B. Linowitz) (2017) Geometriae Dedicata, Volume 188, no. 1. (2015) arXiv Preprint
 Systolic Surfaces of Arithmetic Hyperbolic 3Manifolds (joint w. B. Linowitz)
To appear in
In the Tradition of AhlforsBers, VII
(2015) arXiv Preprint
 The length spectra of arithmetic hyperbolic 3manifolds and their totally geodesic surfaces
(joint w. B. Linowitz and P. Pollack)
(2015) New York Journal of Math, Volume 21, 955972.
(2015) arXiv Preprint
 Totally Geodesic Spectra of Arithmetic Hyperbolic Spaces
To appear in
Transactions of the AMS (2014) arXiv Preprint
 Division Algebras With Infinite Genus
(2014) Bulletin of the London Mathematical Society, Volume 46, no. 3, 463468. (2013) arXiv Preprint
Unpublished Manuscripts 
