I am interested in analytic number theory, circle/sphere packings, thin groups, and quaternion algebras. My current work is at the intersection of those topics, studying the classification/construction problem for integral crystallographic packings.

I also have another project looking at the applications of model theory to the Ulam sequence, which was originally posed as a problem in additive number theory.

## Papers:

- The Unreasonable Rigidity of Ulam Sets. arXiv:1711.00145
- Quaternion Orders and Superpackings. arXiv:1708.03405
- Orders of Quaternion Algebras with Involution. Journal of Number Theory, 183 (2018) 249-268.
- A Corrigendum to Unreasonable Slightness. The American Mathematical Monthly, 123(5) (2016) 482-85.

## Talks:

- Dartmouth College.
*Quaternion Algebras and Integral Sphere Packings*. Feb. 2017. Slides available here: quaternion-algebras-and-sphere-packings. - University of Colorado, Boulder.
*Quaternion Algebras and Integral Sphere Packings*. Oct. 2016.

## REU Students:

- 2017 SUMRY (
*The Unreasonable Rigidity of Ulam Sets)*:- Joshua Hinman
- Borys Kuca
- Alexander Schlesinger

- 2016 SUMRY (
*Embeddings of Imaginary Quadratic Fields into Rational Quaternion Algebras*):- Alexander Schlesinger
- Rose Mintzer-Sweeney
- Katherine Xiu

- 2015 DIMACS REU (
*Cymatics-Chlandi plates*):- Lolly Kenigsberg