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

## Publications

1. Computing Zeta Functions of Cyclic Covers in Large Characteristic (with Vishal Arul, Alex Best, Richard Magner, and Nicholas Triantafillou )
presented at ANTS (Algorithmic Number Theory Symposium)
arXiv:1806.02262, SageMath implementation
2. Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in $p$-adic cohomology (with David Harvey and Kiran Kedlaya)
presented at ANTS (Algorithmic Number Theory Symposium)
arXiv:1806.00368
3. Rigorous computation of the endomorphism ring of a Jacobian (with Nicolas Mascot, Jeroen Sijsling, and John Voight )
to appear in Mathematics of Computation.
arXiv:1705.09248, SageMath/Magma implementation
4. On the arithmetic of a family of degree-two K3 surfaces (with Florian Bouyer, Dino Festi, Chris Nicholls, and Mckenzie West )
Mathematical Proceedings (2018).
DOI, arXiv:1703.02127
5. On the distribution of the Picard ranks of the reductions of a K3 surface (with Andreas-Stephan Elsenhans and Jörg Jahnel )
submitted
arXiv:1610.07823.
6. 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(2) (2018).
DOI, arXiv:1610.00164.
7. Effective computations of Hasse-Weil zeta functions
Ph.D. thesis pdf
8. 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.
9. 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.
10. A search for Wilson primes (with Robert Gerbicz and David Harvey)
Mathematics of Computation 82 (2014), 3071-3091.
DOI, arXiv:1209.3436.
11. Faster deterministic integer factorization (with David Harvey)
Mathematics of Computation 83 (2014), 339-345.
DOI, arXiv:1201.2116.