**[ Papers ]**

Details about my publications are kept more up to date on my cv.

- A Rigid Analytic Proof that the Abel-Jacobi map Extends to Compact-Type Models, Canadian Mathematical Bulletin, 67(3):648–654,2024 (with J. Rabinoff)
- The Theory of the Entire Algebraic Functions, Int. Math. Res. Not. IMRN, (10):8609–8617, 2024 (with E. Hrushovski)
- Angle Ranks of Abelian Varieties over Finite Fields ,Math. Ann.389(2024), no.1, 169–185, 2024 (with K. Kedlaya, and D. Zureick-Brown)
- Isogeny classes of Abelian Varieties over Finite Fields in the LMFDB,Simons Symposia. Springer, 2022 (with K. Kedlaya, D. Roe, and C. Vincent)
- Counterexamples to a Conjecture of Ahmadi and Shparlinski Exp. Math.32, no.3, 540–544,(2023) (with K. Kedlaya, D. Roe, and C. Vincent)
- Deligne-Illusie Classes as Arithmetic Kodaira-Spencer Classes, Journal de Theorie de Nombre de Bordeaux 31, (2019) 371-383 (with D. Zureick-Brown)
- Total p-differential on Schemes Over Z/p^2, Journal of Algebra 524, 110-123 (2019) (with E. Katz, J. Rabinoff, and D. Zureick-Brown)
- Examples of Geometric Bombieri-Lang-Noguchi Outside of Mordell-Lang: Non-rigid Varieties with Ample but Not Globally Generated Cotangent Bundle, Journal of Number Theory 175 (2017) 158–166
- Arithmetic Differential Equations on GL_n I: Differential Cocycles (with A. Buium), Journal of Algebra 454, (2016): 273-291
- Average Bits of 3^n in Binary, Wieferich primes and a Conjecture of Erdos (with D. Weirich) Journal of Number Theory 158, January (2016): 268-280
- Arithmetic Differential Equations on GL_n III: Galois theory (with A. Buium), Selecta Mathematica 22 (2), (2016): 529-552
- Arithmetic Differential Equations on GL_n, II: Arithmetic Lie-Cartan Theory (with A. Buium), Selecta Mathematica 22 (2), (2016): 447-528
- Positivity and Lifts of the Frobenius Math. Res. Lett. 21 (2014) no. 02: 1-7
- Lifted Torsors of Lifts of the Frobenius for Curves (Thesis)

**[ Preprints ]**

- Order One Differential Equations on Non-isotrivial Algebraic Curves (with J. Freitag)
- The Basic Theory of Clifford-Bianchi Groups for Hyperbolic n-Space (with A. Hilado, C. Ingalls, A. Logan)
- Ford Spheres in the Clifford-Bianchi Setting (with S. Backmann, A. Hilado, and V. Potter)

**[Preprints related to the ABC Conjecture]**

- Log-Kummer Correspondences and The Third Indeterminacy (with A. Hilado) --- Appendix of Interpretation Tables
- The Statement of Mochizuki's Corollary 3.12, Initial Theta Data, and the First Two Indeterminacies, (with A. Hilado)
- Probabilistic Szpiro, Baby Szpiro, and Explicit Szpiro from Mochizuki's Corollary 3.12, (with A. Hilado)

**[In Preparation]**

- Non-representability of arithmetic arc spaces (with L. E. Miller and E. Overton-Walker)