← Taylor Dupuy

Papers

Details about my publications are also kept on my CV.

Published

• Labeling Abelian Varieties over Finite Fields, in LuCaNT: LMFDB, Computation, and Number Theory, Contemporary Mathematics, vol. 840, AMS, 2025 (with E. Costa, S. Marseglia, D. Roe, and C. Vincent) — AMS.
• 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 (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 Théorie des Nombres de Bordeaux 31, 2019, 371–383 (with D. Zureick-Brown).
• Total p-Differentials on Schemes Over Z/p², 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, 158–166, 2017.
• Arithmetic Differential Equations on GL_n I: Differential Cocycles, Journal of Algebra 454, 273–291, 2016 (with A. Buium).
• Average Bits of 3^n in Binary, Wieferich Primes and a Conjecture of Erdős, Journal of Number Theory 158, 268–280, 2016 (with D. Weirich).
• Arithmetic Differential Equations on GL_n III: Galois Theory, Selecta Mathematica 22(2), 529–552, 2016 (with A. Buium).
• Arithmetic Differential Equations on GL_n II: Arithmetic Lie-Cartan Theory, Selecta Mathematica 22(2), 447–528, 2016 (with A. Buium).
• Positivity and Lifts of the Frobenius, Math. Res. Lett. 21, no. 02, 1–7, 2014.
• Lifted Torsors of Lifts of the Frobenius for Curves (thesis).

Preprints

• The Dimension Conjecture Implies The Jacobi Bound Conjecture (with D. Zureick-Brown).
• The Jacobi Bound Conjecture for Generically Reduced Differential Schemes (with D. Zureick-Brown).
• Ordinary Abelian Varieties: Isogeny Graphs and Polarizations (with E. Costa, S. Marseglia, D. Roe, and C. Vincent).
• 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).

ABC Conjecture Manuscripts

• The Statement of Mochizuki's Corollary 3.12: Initial Theta Data, The Ramanujan Journal, 2025 (with A. Hilado). ( journal copy )
• The Statement of Mochizuki's Corollary 3.12: the First Two Indeterminacies (with A. Hilado),arXiv:2004.13228.
• Log-Kummer Correspondences and the Third Indeterminacy (with A. Hilado) — appendix of interpretation tables.
• Probabilistic Szpiro, Baby Szpiro, and Explicit Szpiro from Mochizuki's Corollary 3.12 (with A. Hilado).

Course notes

• Algebraic Theory of Differential Equations — book-length notes from the course at UVM, Fall 2022.
• Algebraic Curves and Surfaces — book-length notes from the course at UVM, Fall 2021.

Miscellaneous notes

See also my YouTube channel for expository and research videos. Some additional notes appear in the talks page.

• Automorphisms of the Affine Line over Non-Reduced Rings (not intended for publication).
• Quick introduction to p-jets.
• How units are often used to determine mathematical models (as explained to me by Hannes Schenk).
• Deninger Cohomology Theories.
• Belyi's Theorem (half of it as explained to me by Zach Scherr).
• Quadratic Reciprocity — notes from when I subbed for Danielle and didn't finish in class.
• Model Theory notes — taken from Thomas Scanlon's course at the CUNY Arithmetic Dynamics Conference, July 2010.
• Eichler-Shimura (weight two) — a crash course in modular parametrizations of elliptic curves (the converse of what Wiles proved, the easy part).
• History of Jet Spaces and Diophantine Geometry — a section excluded from my research statement.
• p-adic and Dyadic Harmonic Analysis — Calderón-Zygmund operators.
• Harmonic Analysis, Metric Spaces and PDEs (edited with Lucas Chaffee, Rafael Espinosa, Jarod Hart, Anna Kairema, Lyudmila Korobenko).
• Zeros of Analytic Functions That Don't Have Zeros (Szegő Curves) — undergraduate work with Ken McLaughlin at the University of Arizona (VIGRE), with movies.
• Interpretations in IUT.

Some of the work above was supported by the National Science Foundation, DMS-2401570. Opinions, findings, and conclusions or recommendations expressed are those of the author and do not necessarily reflect the views of the National Science Foundation or the University of Vermont.