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

## Publications

1. Rigorous computation of the endomorphism ring of a Jacobian (with Nicolas Mascot, Jeroen Sijsling, and John Voight )
submitted
arXiv:1705.09248, SageMath/Magma implementation
2. 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
3. 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.
4. 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 (2017).
DOI, arXiv:1610.00164.
5. Effective computations of Hasse-Weil zeta functions
Ph.D. thesis pdf
6. 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.
7. 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.
8. A search for Wilson primes (with Robert Gerbicz and David Harvey)
Mathematics of Computation 82 (2014), 3071-3091.
DOI, arXiv:1209.3436.
9. Faster deterministic integer factorization (with David Harvey)
Mathematics of Computation 83 (2014), 339-345.
DOI, arXiv:1201.2116.