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

Ongoing Projects

Publications

  1. Computing Zeta Functions of Cyclic Covers in Large Characteristic (with Vishal Arul, Alex Best, Richard Magner, and Nicholas Triantafillou )
    presented at ANTS (Algorithmic Number Theory Symposium)
    arXiv:1806.02262, SageMath implementation
  2. Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in $p$-adic cohomology (with David Harvey and Kiran Kedlaya)
    presented at ANTS (Algorithmic Number Theory Symposium)
    arXiv:1806.00368
  3. 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
  4. On the arithmetic of a family of degree-two K3 surfaces (with Florian Bouyer, Dino Festi, Chris Nicholls, and Mckenzie West )
    Mathematical Proceedings (2018).
    DOI, arXiv:1703.02127
  5. On the distribution of the Picard ranks of the reductions of a K3 surface (with Andreas-Stephan Elsenhans and Jörg Jahnel )
    submitted
    arXiv:1610.07823.
  6. 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 162(2) (2018).
    DOI, arXiv:1610.00164.
  7. Effective computations of Hasse-Weil zeta functions
    Ph.D. thesis pdf
  8. 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.
  9. 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.
  10. A search for Wilson primes (with Robert Gerbicz and David Harvey)
    Mathematics of Computation 82 (2014), 3071-3091.
    DOI, arXiv:1209.3436.
  11. Faster deterministic integer factorization (with David Harvey)
    Mathematics of Computation 83 (2014), 339-345.
    DOI, arXiv:1201.2116.

Software

Talks

Other