Research

Supersingular curves of genus five for primes congruent to three modulo four, with Rachel Pries, preprint. [arxiv]
Iwasawa theory of Frobenius-torsion class group schemes, with Bryden Cais, Joe Kramer-Miller, and James Upton, preprint. [arxiv]
Higher a-numbers in Zp-towers via Counting Lattice Points, with Jack Hsieh, Rakesh Rivera, Vincent Tran, James Upton, Carol Wu, preprint. [arxiv]
This started as a student project at PROMYS 2023.
Doubly isogenous curves of genus two with a rational action of D₆, with Everett W. Howe, Andrew V. Sutherland, and José Felipe Voloch, preprint. [arxiv][code]
Lifting G-Valued Galois Representations when l ≠ p, with Sean Cotner and Shiang Tang, Forum of Mathematics, Sigma, 12, 2024, p. e109. [arxiv][journal]
Failing to hash into supersingular isogeny graphs, with Ross Bowden, Javad Doliskani, Tako Boris Fouotsa, Steven D. Galbraith, Sabrina Kunzweiler, Simon-Philipp Merz, Christophe Petit, Benjamin Smith, Katherine E. Stange, Yan Bo Ti, Christelle Vincent, José Felipe Voloch, Charlotte Weitkämper, and Lukas Zobernig, The Computer Journal, Volume 67, Issue 8, August 2024, Pages 2702–2719. [arXiv] [journal] [CFAIL conference]
Iwasawa Theory for p-torsion Class Group Schemes in Characteristic p, with Bryden Cais, Nagoya Mathematical Journal , Volume 250 , June 2023 , pp. 298 – 351. [arXiv] [journal] [Magma code]
Doubly isogenous genus-2 curves with D₄-action, with Vishal Arul, Steven R. Groen, Everett W. Howe, Wanlin Li, Vlad Matei, Rachel Pries, and Caleb Springer, Math. Comp. 93 (2024), 347-381. [arXiv] [journal][Magma Code]

Recovering affine curves over finite fields from L-functions, with José Felipe Voloch, Pacific Journal of Mathematics 314-1 (2021), 1–28. [arXiv] [journal]

G-Valued Crystalline Deformation Rings in the Fontaine-Laffaille Range, with Brandon Levin, Compositio Mathematica, Volume 159, Issue 8, August 2023, pp. 1791 – 1832. [arXiv] [journal]

Tamely Ramified Covers of the Projective Line with Alternating and Symmetric Monodromy, with Renee Bell, William Chen, and Yuan Liu, Algebra & Number Theory,
Vol. 16 (2022), No. 2, 393–446. [arXiv] [journal]

Recovering Algebraic Curves from L-functions of Hilbert Class Fields, with José Felipe Voloch, Research in Number Theory 6, 43 (2020). [arXiv] [journal]

Realizing Artin-Schreier Covers of Curves with Minimal Newton Polygons
in Positive Characteristic, with Rachel Pries, Journal of Number Theory, Volume 214, (2020) pages 240-250. [arXiv], [journal]

Realizing Artin-Schreier Covers with Minimal a-numbers in Positive
Characteristic, with Fiona Abney-McPeek, Hugo Berg, Sun Mee Choi,
Viktor Fukala, Miroslav Marinov, Theo Müller, Paweł
Narkiewicz, Rachel Pries, Nancy Xu, and Andrew Yuan, Involve, a Journal of Mathematics 15-4 (2022), 559–590. [arXiv] [journal ]
This incorporates student projects from PROMYS 2019.

a-Numbers in Artin-Schreier Covers, with Bryden Cais, Algebra & Number Theory, Vol. 14 (2020), No. 3, 593–653. [arXiv] [journal] (MAGMA computations)

G-Valued Galois Deformation Rings when l ≠ p, with Stefan Patrikis,
Mathematical Research Letters, Vol. 26, No. 4 (2019), pp. 973-990. [arXiv], [journal]

Minimally Ramified Deformations when l ≠ p. Compositio Mathematica, Volume 155 / Issue 1 (2019) pages 1-37. [arXiv], [journal]

Producing Geometric Deformations of Orthogonal and Symplectic Galois Representations. Journal of Number Theory, Volume 195, (2019) pages 115-158.
[arXiv] [journal]

Geometric Deformations of Orthogonal and Symplectic Galois Representations is the paper version of my thesis. It has been broken up into the two papers above for publication.

Evaluation of Cubic Twisted Kloosterman Sheaf Sums, with Anastassia Etropolski and Amanda Hittson. International Journal of Number Theory, 6 (2010), pages 1349-1365. [pdf] [journal]