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.



  • 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