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 Γ-packings.

## Papers:

- Quaternion Orders and Superpackings. arXiv:1708.03405
- Orders of Quaternion Algebras with Involution. Journal of Number Theory (to appear) arXiv:1612.07711
- 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

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