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

Research Publications

1. 17T7 is a Galois group over the rationals
   with Raymond van Bommel, Noam D. Elkies, Timo Keller, Sam Schiavone, and John Voight
   [ arXiv Code ]
2. Hypergeometric L-functions in average polynomial time, II
   with Kiran Kedlaya, and David Roe
   to appear in Sixteenth Algorithmic Number Theory Symposium, Research in Number Theory
   [ arXiv Code ]
3. A database of basic numerical invariants of Hilbert modular surfaces
   with Eran Assaf, Angelica Babei, Ben Breen, Juanita Duque-Rosero, Aleksander Horawa, Jean Kieffer, Avinash Kulkarni, Grant Molnar, Sam Schiavone, and John Voight
   LMFDB, Computation, and Number Theory (LuCaNT), Contemporary Mathematics 796 (2024), 285–312
   [ arXiv DOI Code MR ]
4. Computing isogeny classes of typical principally polarized abelian surfaces over the rationals
   with Raymond van Bommel, Shiva Chidambaram, and Jean Kieffer
   LMFDB, Computation, and Number Theory (LuCaNT), Contemporary Mathematics 796 (2024), 187–214
   [ arXiv DOI Code MR ]
5. Counting points on smooth plane quartics
   with David Harvey, and Andrew V. Sutherland
   Fifteenth Algorithmic Number Theory Symposium, Research in Number Theory 9 (2023), no 1
   [ arXiv DOI Code MR ]
6. Abelian varieties of prescribed order over finite fields
   with Raymond van Bommel, Wanlin Li, Bjorn Poonen, and Alexander Smith
   to appear in Mathematische Annalen
   [ arXiv Code ]
7. Hypergeometric L-functions in average polynomial time
   with Kiran Kedlaya, and David Roe
   Fourteenth Algorithmic Number Theory Symposium, Open Book Series 4 (2020), 143–159
   [ arXiv DOI Code MR ]
8. Effective obstruction to lifting Tate classes from positive characteristic
   with Emre Can Sertöz
   Arithmetic geometry, number theory, and computation, Simons Symposia (2021), 293–333
   [ arXiv DOI Offprint Code MR ]
9. Computing classical modular forms
   with Alex J. 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 (2021), 123-213
   [ arXiv DOI Offprint Errata Code ]
10. 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 (2021), 259–276
    [ arXiv DOI Offprint MR ]
11. Arithmetic invariants from Sato-Tate moments
    with Francesc Fité, and Andrew V. Sutherland
    Comptes Rendus Mathematique, 357 (2019), 823-826
    [ arXiv DOI MR Zbl ]
12. Zen and the Art of Database Maintenance
    with David Roe
    Arithmetic geometry, number theory, and computation, Simons Symposia (2021), 277–292
    [ DOI Offprint MR ]
13. Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms
    with Davide Lombardo, and John Voight
    Research in Number Theory, 7 (2021), no. 3, 46
    [ arXiv DOI Offprint MR Zbl ]
14. Computing Zeta Functions of Cyclic Covers in Large Characteristic
    with Vishal Arul, Alex J. Best, Richard Magner, and Nicholas Triantafillou
    Thirteenth Algorithmic Number Theory Symposium, The Open Book Series 2 (2019), 37–53
    [ arXiv DOI Code MR ]
15. 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, Open Book Series 2 (2019), 221–238
    [ arXiv DOI Code MR ]
16. Rigorous computation of the endomorphism ring of a Jacobian
    with Nicolas Mascot, Jeroen Sijsling, and John Voight
    Mathematics of Computation, 88 (2019), 1303-1339
    [ arXiv DOI Errata Code MR Zbl ]
17. On the arithmetic of a family of degree-two K3 surfaces
    with Florian Bouyer, Dino Festi, Chris Nicholls, and Mckenzie West
    Mathematical Proceedings of the Cambridge Philosophical Society, 166 (2018), no. 3, 523-542
    [ arXiv DOI Code MR Zbl ]
18. On the distribution of the Picard ranks of the reductions of a K3 surface
    with Andreas-Stephan Elsenhan, and Jörg Jahnel
    Research in Number Theory, 6 (2020), no. 3, 27 (2020)
    [ arXiv DOI MR Zbl ]
19. 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 of the Cambridge Philosophical Society, 162 (2018), no. 2, 225–248
    [ arXiv DOI MR Zbl ]
20. Effective computations of Hasse-Weil zeta functions
    Ph.D. thesis, New York University (2015)
    [ Offprint Code ]
21. Variation of Néron-Severi ranks of reductions of K3 surfaces
    with Yuri Tschinkel
    Experimental Mathematics, 23 (2014), 475-481
    [ arXiv DOI Data MR Zbl ]
22. Asymptotic expansions, L-values and a new Quantum Modular Form
    The Ramanujan Journal, 35 (2014), 141-148
    [ arXiv DOI MR Zbl ]
23. A search for Wilson primes
    with Robert Gerbicz, and David Harvey
    Mathematics of Computation, 82 (2014), 3071-3091
    [ arXiv DOI MR Zbl ]
24. Faster deterministic integer factorization
    with David Harvey
    Mathematics of Computation, 83 (2014), 339-345
    [ arXiv DOI MR Zbl ]

Expository Publications

1. Research seminars: a new hope
   with Bjorn Poonen, Andrew V. Sutherland, and David Roe
   Math in the time of corona, Mathematics Online First Collections (2021), 113-115
   [ DOI Code MR ]
2. Étale Cohomology
   M.Sc. thesis, Insituto Superior Técnico (2010)
   [ Offprint ]