Research

MathBases: Indexing and Creating Mathematical Databases
with Katja Berčič, and David Roe
to appear in International Congress on Mathematical Software 2026

Murmurations, Mestre--Nagao sums, and Convolutional Neural Networks for elliptic curves
with Joanna Bieri, Alyson Deines, Kyu-Hwan Lee, David Lowry-Duda, Thomas Oliver, Yidi Qi, and Tamara Veenstra
to appear in Research in Number Theory
[ arXiv ]

Ordinary abelian varieties: isogeny graphs and polarizations
with Taylor Dupuy, Stefano Marseglia, David Roe, and Christelle Vincent
Seventeenth Algorithmic Number Theory Symposium, Research in Number Theory (to appear)
[ arXiv ]

Machine learning the vanishing order of rational $L$-functions
with Joanna Bieri, Girgi Butbaia, Alyson Deines, Kyu-Hwan Lee, David Lowry-Duda, Thomas Oliver, Yidi Qi, and Tamara Veenstra
Advances in Theoretical and Mathematical Physics, Volume 29, Number 8, pages 2381–2401, (2025)
[ arXiv DOI MR ]

Explicit modularity of K3 surfaces with complex multiplication of large degree
with Andreas-Stephan Elsenhan, Jörg Jahnel, and John Voight
LMFDB, Computation, and Number Theory (LuCaNT), Contemporary Mathematics 840 (2026), 103–109
[ arXiv DOI Code Zbl ]

Learning Euler Factors of Elliptic Curves
with Angelica Babei, François Charton, Xiaoyu Huang, Kyu-Hwan Lee, David Lowry-Duda, Ashvni Narayanan, and Alexey Pozdnyakov
Advances in Theoretical and Mathematical Physics, Volume 29, Number 8, pages 2327–2351, (2025)
[ arXiv DOI MR ]

Curve equations from expansions of 1-forms at a nonrational point
with Raymond van Bommel, Bjorn Poonen, and Padmavathi Srinivasan
LMFDB, Computation, and Number Theory (LuCaNT), Contemporary Mathematics 840 (2026), 345–354
[ arXiv DOI ]

Learning Fricke signs from Maass form Coefficients
with Joanna Bieri, Girgi Butbaia, Alyson Deines, Kyu-Hwan Lee, David Lowry-Duda, Thomas Oliver, Yidi Qi, and Tamara Veenstra
Advances in Theoretical and Mathematical Physics, Volume 29, Number 8, pages 2403–2423, (2025)
[ arXiv DOI MR ]

Labeling abelian varieties over finite fields
with Taylor Dupuy, Stefano Marseglia, David Roe, and Christelle Vincent
LMFDB, Computation, and Number Theory (LuCaNT), Contemporary Mathematics 840 (2026), 277–283
[ arXiv DOI Code ]

17T7 is a Galois group over the rationals
with Raymond van Bommel, Noam D. Elkies, Timo Keller, Sam Schiavone, and John Voight
to appear in Algebra and Number Theory
[ arXiv Code ]

Hypergeometric L-functions in average polynomial time, II
with Kiran Kedlaya, and David Roe
Sixteenth Algorithmic Number Theory Symposium, Research in Number Theory 11, 32 (2025)
[ arXiv DOI Offprint Code MR Zbl ]

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 Zbl ]

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 Zbl ]

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 Offprint Code MR Zbl ]

Abelian varieties of prescribed order over finite fields
with Raymond van Bommel, Wanlin Li, Bjorn Poonen, and Alexander Smith
Mathematische Annalen, Volume 392, pages 1167–1202, (2025)
[ arXiv DOI Code MR ]

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 Zbl ]

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 Zbl ]

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), 131-213
[ arXiv DOI Offprint Errata Code MR Zbl ]

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 Zbl ]

Arithmetic invariants from Sato-Tate moments
with Francesc Fité, and Andrew V. Sutherland
Comptes Rendus Mathematique, 357 (2019), 823-826
[ 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 Zbl ]

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 Zbl ]

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 Zbl ]

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 ]

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 ]

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 ]

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, 165 (2018), no. 2, 225–248
[ arXiv DOI MR Zbl ]

Effective computations of Hasse-Weil zeta functions
Ph.D. thesis, New York University (2015)
[ Offprint Code MR ]

Variation of Néron-Severi ranks of reductions of K3 surfaces
with Yuri Tschinkel
Experimental Mathematics, 23 (2014), 475-481
[ arXiv DOI Data MR Zbl ]

Asymptotic expansions, L-values and a new Quantum Modular Form
The Ramanujan Journal, 35 (2014), 141-148
[ arXiv DOI MR Zbl ]

A search for Wilson primes
with Robert Gerbicz, and David Harvey
Mathematics of Computation, 83 (2014), 3071-3091
[ arXiv DOI MR Zbl ]

Faster deterministic integer factorization
with David Harvey
Mathematics of Computation, 83 (2014), 339-345
[ arXiv DOI MR Zbl ]

Research Publications

Expository Publications