My research interests are centered around effective methods in arithmetic geometry, arithmetic statistics, and number theory.

Algebra and Number Theory seminar

Ongoing Projects


  1. Rigorous computation of the endomorphism ring of a Jacobian (with Nicolas Mascot, Jeroen Sijsling, and John Voight )
    to appear in Mathematics of Computation,
    arXiv:1705.09248, SageMath/Magma implementation
  2. On the arithmetic of a family of degree-two K3 surfaces (with Florian Bouyer, Dino Festi, Chris Nicholls, and Mckenzie West )
    to appear in Mathematical Proceedings,
  3. On the distribution of the Picard ranks of the reductions of a K3 surface (with Andreas-Stephan Elsenhans and Jörg Jahnel )
    to appear in Algebra & Number Theory,
  4. Traces, High powers and One level density for families of curves over finite fields (with Alina Bucur, Chantal David, João Guerreiro, David Lowry-Duda )
    Mathematical Proceedings (2017), 1-24.
    DOI, arXiv:1610.00164.
  5. Effective computations of Hasse-Weil zeta functions
    Ph.D. thesis pdf
  6. Variation of Néron-Severi ranks of reductions of K3 surfaces (with Yuri Tschinkel)
    Experimental Mathematics 23 (2014), 475-481.
    DOI, arXiv:1405.2265, raw data.
  7. Asymptotic expansions, $L$-values and a new Quantum Modular Form (with Korneel Debaene and João Guerreiro)
    The Ramanujan Journal 35 (2014), 141-148.
    DOI, arXiv:1311.3469.
  8. A search for Wilson primes (with Robert Gerbicz and David Harvey)
    Mathematics of Computation 82 (2014), 3071-3091.
    DOI, arXiv:1209.3436.
  9. Faster deterministic integer factorization (with David Harvey)
    Mathematics of Computation 83 (2014), 339-345.
    DOI, arXiv:1201.2116.