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


  1. Computing classical modular forms (with Alex Best, Jonathan Bober, Andrew R. Booker, John Cremona, Maarten Derickx, David Lowry-Duda, Min Lee, David Roe, Andrew V. Sutherland, and John Voight )
  2. Restrictions on Weil polynomials of Jacobians of hyperelliptic curves (with Ravi Donepudi, Ravi Fernando, Valentijn Karemaker, Caleb Springer, and Mckenzie West)
  3. Arithmetic invariants from Sato-Tate moments (with Francesc Fité and Andrew V. Sutherland)
    Comptes Rendus Mathematique
    DOI, arXiv:1910.00518
  4. Zen and the Art of Database Maintenance (with David Roe)
  5. Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms (with Davide Lombardo and John Voight )
  6. Computing Zeta Functions of Cyclic Covers in Large Characteristic (with Vishal Arul, Alex Best, Richard Magner, and Nicholas Triantafillou )
    Thirteenth Algorithmic Number Theory Symposium (ANTS XIII), Open Book Series 2 (2019), 37–53.
    DOI, arXiv:1806.02262, SageMath implementation
  7. Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in $p$-adic cohomology (with David Harvey and Kiran Kedlaya)
    Thirteenth Algorithmic Number Theory Symposium (ANTS XIII), Open Book Series 2 (2019), 221–238.
    DOI, arXiv:1806.00368
  8. Rigorous computation of the endomorphism ring of a Jacobian (with Nicolas Mascot, Jeroen Sijsling, and John Voight )
    Mathematics of Computation 88 (2019), 1303-1339
    DOI, arXiv:1705.09248, SageMath/Magma implementation
  9. On the arithmetic of a family of degree-two K3 surfaces (with Florian Bouyer, Dino Festi, Chris Nicholls, and Mckenzie West )
    Mathematical Proceedings 166 (2018), no. 3, 523-542.
    DOI, arXiv:1703.02127
  10. On the distribution of the Picard ranks of the reductions of a K3 surface (with Andreas-Stephan Elsenhans and Jörg Jahnel )
  11. 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 (2018), no. 2, 225–248
    DOI, arXiv:1610.00164.
  12. Effective computations of Hasse-Weil zeta functions
    Ph.D. thesis pdf
  13. 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.
  14. 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.
  15. A search for Wilson primes (with Robert Gerbicz and David Harvey)
    Mathematics of Computation 82 (2014), 3071-3091.
    DOI, arXiv:1209.3436.
  16. Faster deterministic integer factorization (with David Harvey)
    Mathematics of Computation 83 (2014), 339-345.
    DOI, arXiv:1201.2116.