# Mathematics Research

**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**

- Systole inequalities up congruence towers for arithmetic locally symmetric spaces (joint w. S. Lapan and B. Linowitz)
- Counting Commensurability Classes of Codimension One Subspaces (joint w. B. Linowitz)
*(in preparation)*

- Totally Geodesic Spectra of Quaternionic Hyperbolic Orbifolds

**Publications**

- Constructing Geometrically Equivalent Hyperbolic Orbifolds (joint w. D.B. McReynolds and M. Stover)
- On the isospectral orbifold-manifold problem for nonpositively curved locally symmetric spaces (joint w. B. Linowitz)
- Systolic Surfaces of Arithmetic Hyperbolic 3-Manifolds (joint w. B. Linowitz)
- The length spectra of arithmetic hyperbolic 3-manifolds and their totally geodesic surfaces (joint w. B. Linowitz and P. Pollack)
- Totally Geodesic Spectra of Arithmetic Hyperbolic Spaces
- Division Algebras With Infinite Genus

**Unpublished Manuscripts**

- On The Totally Geodesic Commensurability Spectrum of Arithmetic Locally Symmetric Spaces