Research Interests
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Explicit number theory/diophantine geometry​
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Point counting on elliptic curves & abelian varieties​
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Applications to post-quantum cryptography
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Diophantine equations and approximation​
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S-units equations and algebraic tori ​
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Continued fractions/badly approximable numbers
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Definability and decidability
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Hilbert's Tenth Problem over arithmetically significant rings​
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Computational complexity of decision problems
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Algebraic Model Theory​
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Transfer principles and o-minimality as applied to algebraic geometry
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Publications
Published/Accepted:
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Discrete m-functions with Doubly Palindromic Continued Fraction Coefficients (with Brian Simanek) — accepted for publication
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Continued Fractions: an Arithmetic and Analytic Study
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Baylor Repository: https://doi.org/10.48550/arXiv.2205.06653
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Preprints
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First-Order Definability of Darmon Points in Number Fields (with Juan Pablo De Rasis) - in preparation
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Efficient Zero-Knowledge Outer Products and Matrix Multiplication (with Jessica Bennett, Shuhong Gao, Aram Lindroth, Emily Sundberg, & Marvin Jones) - in preparation
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All Evils Great and Small (with Levi Durham) - in preparation
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Philosophy of religion, formal epistemology, and decision theory
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