My research interests land in the realm of using number theoretic tools in hyperbolic geometry.  In particular, my current projects include:

• Generalization of associated quaternion algebras over SL(2,C)-character varieties

• Totally geodesic surfaces in hyperbolic 3-manifolds

• Pseudomodular groups and arithmetic dimension

I've also recently been intrigued by learning more about Brauer groups as well as character varieties over matrix groups other than SL(2,C).

Papers

4. Geodesic surfaces in the complement of knots with small crossing number
with Khanh Le. New York Journal of Mathematics 29 (2023), 363 – 401. [NYJM]

3. Totally geodesic surfaces in twist knot complements
with Khanh Le.  Pacific Journal of Mathematics 319-1 (2022), 153 – 179. [arXiv]

2. Some dual definite integrals for Bessel functions of the first kind
with H.S. Cohl and Sean Nair.  Scientia, Series A: Mathematical Science, no. 27 (2016) [arXiv]

1. Fourier and Gegenbauer Expansions for a Fundamental Solution of Laplace's Equation in Hyperspherical Geometry
with H.S. Cohl.  SIGMA, no. 11 (2015) [arXiv]

Talks