Research Interests

Explicit number theory/diophantine geometry
- Point counting on elliptic curves & abelian varieties
- Applications to post-quantum cryptography
Diophantine equations and approximation
- S-units equations and algebraic tori
- Continued fractions/badly approximable numbers
Definability and decidability
- Hilbert's Tenth Problem over arithmetically significant rings
- Computational complexity of decision problems
Algebraic Model Theory
- Transfer principles and o-minimality as applied to algebraic geometry

Publications

Discrete m-functions with Doubly Palindromic Continued Fraction Coefficients (with Brian Simanek) — accepted for publication
- arXiv: https://doi.org/10.48550/arXiv.2205.06653
Continued Fractions: an Arithmetic and Analytic Study
- Baylor Repository: https://doi.org/10.48550/arXiv.2205.06653

First-Order Definability of Darmon Points in Number Fields (with Juan Pablo De Rasis) - submission in progress
- arXiv: https://doi.org/10.48550/arXiv.2410.03033
Efficient Zero-Knowledge Outer Products and Matrix Multiplication (with Jessica Bennett, Shuhong Gao, Aram Lindroth, Emily Sundberg, & Marvin Jones) - in preparation
All Evils Great and Small (with Levi Durham) - submission in progress
- Philosophy of religion, formal epistemology, and decision theory

What is Completeness? - Introductory notes on Gödel's Completeness Theorem and applications of complete theories to graph theory, algebra, and geometry, developed for OSU's What is? seminar.