Research

Research Interests

I am interested in number theory, arithmetic geometry, and arithmetic statistics.

My research program centers on the study of objects that arise in cohomology from the perspective of arithmetic statistics. In particular, my work focuses on exploring connections between Selmer groups of elliptic curves and Selmer groups of number fields.

I am also interested in effective methods for computation with algebraic objects. A large portion of my research focuses on advancing explicit methods for Hilbert modular forms.

Papers

A database of basic numerical invariants of Hilbert modular surfaces (with Eran Assaf, Angelica Babei, Edgar Costa, Juanita Duque-Rosero, Aleksander Horawa, Jean Kieffer, Avinash Kulkarni, Grant Molnar, Sam Schiavone, and John Voight), Submitted, (2023)
The 2-Selmer group of S_n-number fields of even degree, Submitted, (2022)
On unit signatures and narrow class groups of odd abelian number fields: Galois structure and heuristics (with Ila Varma and John Voight), accepted to Transactions of the American Mathematical Society, (2021)
Wild ramification in a family of low-degree extensions arising from iteration (with Rafe Jones, Tommy Occhipinti, and Michelle Yuen), JP Journal of Algebra, Number Theory and Applications 37, 69-104, (2015)

Preprints

An explicit trace formula for Hilbert modular forms, In preparation, (2023)
On local algebras and the genus theory of S_n number fields, (with Erik Holmes and Angelica Babei), In preparation.
Fourier transforms and related numerical experiments. (with Daryl R. Deford, Jason D. Linehan, Daniel N. Rockmore), arXiv:1710.02687, preprint, (2017)

Software

Hilbert Modular Forms (Magma)
Sampling S4 Number Fields (Magma)
Representations of SL(Z/p^nZ) (SageMath)