National Science Foundation logo Supported by the National Science Foundation DMS-2401570.

[ Papers ]

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

  1. A Rigid Analytic Proof that the Abel-Jacobi map Extends to Compact-Type Models, to appear Canadian Mathematical Bulletin, 2024 (with J. Rabinoff)
  2. The Theory of the Entire Algebraic Functions, to appear IMRN, 2024 (with Ehud Hrushovski)
  3. Angle Ranks of Abelian Varieties over Finite Fields ,Mathematische Annalen, pages 1–17, 2023 (with K. Kedlaya, and D. Zureick-Brown)
  4. Isogeny classes of Abelian Varieties over Finite Fields in the LMFDB,Simons Symposia. Springer, 2022 (with K. Kedlaya, D. Roe, and C. Vincent)
  5. Counterexamples to a Conjecture of Ahmadi and Shparlinski Experimental Mathematics, pages 1–5, 2021 (with K. Kedlaya, D. Roe, and C. Vincent)
  6. Deligne-Illusie Classes as Arithmetic Kodaira-Spencer Classes, Journal de Theorie de Nombre de Bordeaux 31, (2019) 371-383 (with D. Zureick-Brown)
  7. 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)
  8. Examples of Geometric Bombieri-Lang-Noguchi Outside of Mordell-Lang: Non-rigid Varieties with Amples but Not Globally Generated Cotangent Bundle, Journal of Number Theory 175 (2017) 158–166
  9. Arithmetic Differential Equations on GL_n I: Differential Cocycles (with A. Buium), Journal of Algebra 454, (2016): 273-291
  10. 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
  11. Arithmetic Differential Equations on GL_n III: Galois theory (with A. Buium), Selecta Mathematica 22 (2), (2016): 529-552
  12. Arithmetic Differential Equations on GL_n, II: Arithmetic Lie-Cartan Theory (with A. Buium), Selecta Mathematica 22 (2), (2016): 447-528
  13. Positivity and Lifts of the Frobenius Math. Res. Lett. 21 (2014) no. 02: 1-7
  14. Lifted Torsors of Lifts of the Frobenius for Curves (Thesis)

[ Preprints ]

  1. Order One Differential Equations on Non-isotrivial Algebraic Curves (with J. Freitag)

[Preprints related to the ABC Conjecture]

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

[In Preparation]

  1. Non-representability of arithmetic arc spaces (with L. E. Miller and E. Overton-Walker)
  2. The Basic Theory of Clifford-Bianchi Groups for Hyperbolic n-Space (with A. Hilado, C. Ingalls, A. Logan
  3. Ford Spheres for Hyperbolic n-Space (with S. Backmann, A. Hilado, and V. Potter)

[ Manuscripts Not Intended For Publication]

  1. Automorphisms of The Affine Line over Non-Reduced Rings