I am interested in analytic number theory, circle/sphere packings, thin groups, and quaternion algebras. My thesis was 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 computable families of integer sequences, which was originally posed as a problem in additive number theory.

## Papers:

- Quaternion Orders and Sphere Packings. Journal of Number Theory (accepted). arXiv:1708.03405
- Rigidity of Ulam Sets and Sequences (co-authored with J. Hinman, B. Kuca, and A. Schlesinger). Involve 12(3) (2019) 521-539.
- The Unreasonable Rigidity of Ulam Sequences (co-authored with J. Hinman, B. Kuca, and A. Schlesinger). Journal of Number Theory 194 (2019) 409-425.
- 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:

- Graduate Center.
*Hyperbolic Isometry Groups and Quaternion Algebras.*Apr. 2019. - Graduate Center.
*(Searching for)**Applications of Orders with Involution.*Mar. 2019. Slides available here. - Bronx Community College.
*Two Impossible Problems and an Impossible One*. Dec. 2018. Slides available here. - Integers 2018.
*Rigidity in the Ulam Sequence*. Oct. 2018. Slides available here. - New York Logic Model Seminar at CUNY.
*Rigidity in the Ulam Sequence.*Sep. 2018. - CANT at CUNY.
*Rigidity in the Ulam Sequence*. May 2018. - Rutgers University.
*Connections between Integral Sphere Packings and Quaternion Algebras.*May 2018. Slides available here. - Dartmouth College.
*Quaternion Algebras and Integral Sphere Packings*. Feb. 2017. - 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