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.



  • 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