All of my research involves number theory of various flavors. I am very interested in how sub-rings of quaternion algebras over number fields can be used to construct groups, manifolds, and sphere packings. I also have interest in additive number theory and logic.



  • New Trends in Quaternions and Octonions (virtual). Is Unreasonable Slightness a General Phenomenon?. Nov. 2021.
  • Rutgers University (virtual). Is Unreasonable Slightness a General Phenomenon?. Nov. 2021. Slides available here.
  • CANT 2020 (virtual). A Twisted Euclidean Algorithm. May. 2020.
  • UC Davis (virtual). Algebraic Invariants of Hyperbolic 4-Orbifolds. May. 2020.
  • Graduate Center. The Quaternion-Bianchi Dictionary. Nov. 2019.
  • Illustrating Number Theory and Algebra (at ICERM). Euclidean Algorithm in Circle/Sphere Packings. Oct. 2019. Slides available here. Video recording available here.
  • Journées sur les Arithmétiques Faibles (at CUNY). Applications of Model Theory to Families of Integer Sequences. May. 2019
  • 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 Trivial 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