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

A database of basic numerical invariants of Hilbert modular surfaces
with Eran Assaf, Angelica Babei, Ben Breen, Juanita DuqueRosero, Aleksander Horawa, Jean Kieffer, Avinash Kulkarni, Grant Molnar, Sam Schiavone, and John Voight
to appear LMFDB, Computation, and Number Theory (LuCaNT)
[ arXiv ] 
Computing isogeny classes of typical principally polarized abelian surfaces over the rationals
with Raymond van Bommel, Shiva Chidambaram, and Jean Kieffer
to appear LMFDB, Computation, and Number Theory (LuCaNT)
[ arXiv ] 
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 MR ] 
Abelian varieties of prescribed order over finite fields
with Raymond van Bommel, Wanlin Li, Bjorn Poonen, and Alexander Smith
submitted
[ arXiv ] 
Hypergeometric Lfunctions in average polynomial time
with Kiran Kedlaya, and David Roe
Fourteenth Algorithmic Number Theory Symposium, Open Book Series 4 (2020), 143–159
[ arXiv DOI MR ] 
Effective obstruction to lifting Tate classes from positive characteristic
with Emre Sertöz
Arithmetic geometry, number theory, and computation, Simons Symposia (2021), 293–333
[ arXiv DOI Offprint Code MR ] 
Computing classical modular forms
with Alex J. Best, Jonathan Bober, Andrew R. Booker, John Cremona, Maarten Derickx, David LowryDuda, Min Lee, David Roe, Andrew V. Sutherland, and John Voight
Arithmetic geometry, number theory, and computation, Simons Symposia (2021), 123213
[ arXiv DOI Offprint Errata Code ] 
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 ] 
Arithmetic invariants from SatoTate moments
with Francesc Fité, and Andrew V. Sutherland
Comptes Rendus Mathematique, 357 (2019), 823826
[ arXiv DOI MR Zbl ] 
Zen and the Art of Database Maintenance
with David Roe
Arithmetic geometry, number theory, and computation, Simons Symposia (2021), 277–292
[ DOI Offprint MR ] 
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 ] 
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 ] 
Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in padic cohomology
with David Harvey, and Kiran Kedlaya
Thirteenth Algorithmic Number Theory Symposium, Open Book Series 2 (2019), 221–238
[ arXiv DOI MR ] 
Rigorous computation of the endomorphism ring of a Jacobian
with Nicolas Mascot, Jeroen Sijsling, and John Voight
Mathematics of Computation, 88 (2019), 13031339
[ arXiv DOI Errata Code MR Zbl ] 
On the arithmetic of a family of degreetwo K3 surfaces
with Florian Bouyer, Dino Festi, Chris Nicholls, and Mckenzie West
Mathematical Proceedings, 166 (2018), no. 3, 523542
[ arXiv DOI MR Zbl ] 
On the distribution of the Picard ranks of the reductions of a K3 surface
with AndreasStephan Elsenhan, and Jörg Jahnel
Research in Number Theory, 6 (2020), no. 3, 27 (2020)
[ arXiv DOI MR Zbl ] 
Traces, High powers and one level density for families of curves over finite fields
with Alina Bucur, Chantal David, João Guerreiro, and David LowryDuda
Mathematical Proceedings, 162 (2018), no. 2, 225–248
[ arXiv DOI MR Zbl ] 
Effective computations of HasseWeil zeta functions
Ph.D. thesis, New York University (2015)
[ Offprint ] 
Variation of NéronSeveri ranks of reductions of K3 surfaces
with Yuri Tschinkel
Experimental Mathematics, 23 (2014), 475481.
[ arXiv DOI Data MR Zbl ] 
Asymptotic expansions, Lvalues and a new Quantum Modular Form
The Ramanujan Journal, 35 (2014), 141148
[ arXiv DOI MR Zbl ] 
A search for Wilson primes
with Robert Gerbicz, and David Harvey
Mathematics of Computation, 82 (2014), 30713091
[ arXiv DOI MR Zbl ] 
Faster deterministic integer factorization
with David Harvey
Mathematics of Computation, 83 (2014), 339345
[ arXiv DOI MR Zbl ]