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

Publications

  1. Counting points on smooth plane quartics (with David Harvey and Andrew V. Sutherland )
    to appear Research in Number Theory, Fifteenth Algorithmic Number Theory Symposium (ANTS XV)
    arXiv:2208.09890
  2. Abelian varieties of prescribed order over finite fields (with Raymond van Bommel, Wanlin Li, Bjorn Poonen, and Alexander Smith)
    submitted
    arXiv:2106.13651
  3. Hypergeometric L-functions in average polynomial time (with Kiran Kedlaya and David Roe)
    Fourteenth Algorithmic Number Theory Symposium (ANTS XIV), Open Book Series 4 (2020), 143–159
    DOI, arXiv:2005.13640
  4. Effective obstruction to lifting Tate classes from positive characteristic (with Emre Sertöz)
    Arithmetic geometry, number theory, and computation, Simons Symposia
    DOI, arXiv:2003.11037
  5. 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)
    Arithmetic geometry, number theory, and computation, Simons Symposia
    DOI, Errata, arXiv:2002.04717
  6. Restrictions on Weil polynomials of Jacobians of hyperelliptic curves (with Ravi Donepudi, Ravi Fernando, Valentijn Karemaker, Caleb Springer, and Mckenzie West)
    Arithmetic geometry, number theory, and computation, Simons Symposia
    DOI, arXiv:2002.02067
  7. Arithmetic invariants from Sato-Tate moments (with Francesc Fité and Andrew V. Sutherland)
    Comptes Rendus Mathematique
    DOI, arXiv:1910.00518
  8. Zen and the Art of Database Maintenance (with David Roe)
    Arithmetic geometry, number theory, and computation, Simons Symposia
    DOI, pdf
  9. Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms (with Davide Lombardo and John Voight)
    Research in Number Theory 7, 46 (2021)
    DOI, arXiv:1906.02803
  10. 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
  11. 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
  12. 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, Errata, arXiv:1705.09248, SageMath/Magma implementation
  13. 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
  14. On the distribution of the Picard ranks of the reductions of a K3 surface (with Andreas-Stephan Elsenhans and Jörg Jahnel )
    Research in Number Theory 6, 27 (2020)
    DOI, arXiv:1610.07823.
  15. Traces, High powers and one level density for families of curves over finite fields (with Alina Bucur, Chantal David, João Guerreiro, and David Lowry-Duda)
    Mathematical Proceedings 162 (2018), no. 2, 225–248
    DOI, arXiv:1610.00164.
  16. Effective computations of Hasse-Weil zeta functions
    Ph.D. thesis pdf
  17. 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.
  18. 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.
  19. A search for Wilson primes (with Robert Gerbicz and David Harvey)
    Mathematics of Computation 82 (2014), 3071-3091.
    DOI, arXiv:1209.3436.
  20. Faster deterministic integer factorization (with David Harvey)
    Mathematics of Computation 83 (2014), 339-345.
    DOI, arXiv:1201.2116.

Software

Talks

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