Welcome!
I am an associate professor of mathematics at Union College in Schenectady, NY. My research interests are in number theory; in particular, I study Iwasawa theory and p-adic Galois representations associated to modular forms.
When I'm not doing math, I'm usually bouldering, watching Philadelphia sports teams, or spending time with my cats, llamas, chickens, and ducks.
Zachary Porat and I will be co-leading a project as part of the Rethinking Number Theory program for the summer of 2026.
Papers
(Note that preprints may differ from the final published version.)
My Google Scholar Profile
[21] Distinguishing elliptic curves modulo p and identifying images of product representations (with Jessica Bennett, Sasha Kononova, Vincent Macri, Zachary Porat, and Naina Praveen), preprint. arXiv:2608.10880
[20] Iwasawa theory and ranks of elliptic curves in quadratic twist families (with Anwesh Ray), preprint. arXiv:2412:07308
[19] Elliptic curves of conductor 2mp, quadratic twists, and Watkins' conjecture (with Debanjana Kundu), Annales mathématiques du Québec, Vol. 50 (2026), 143--165. https://doi.org/10.1007/s40316-025-00249-8. PDF
[18] On a conjecture of Mazur predicting the growth of Mordell—Weil ranks in Zp-extensions (with Rylan Gajek-Leonard, Debanjana Kundu, and Antonio Lei), Mathematical Research Letters, Vol. 32, Issue 6 (2025), pp. 1877-1912. arXiv:2401.07792
[17] Statistics for anticyclotomic Iwasawa invariants of elliptic curves (with Debanjana Kundu and Anwesh Ray), Mathematische Zeitschrift, Vol. 307, No. 49 (2024). PDF
[16] λ-invariant stability in families of modular Galois representations (with Debanjana Kundu), Research in the Mathematical Sciences, Vol. 10, No. 33 (2023). https://doi.org/10.1007/s40687-023-00396-w. PDF
[15] Polynomials in Fp[x] which commute under composition (with Mayah Teplitskiy), PUMP Journal of Undergraduate Research, Vol. 6 (2023), 102-114. PDF
[14] The vanishing of anticyclotomic µ-invariants for non-ordinary modular forms (with Antonio Lei), Comptes Rendus Mathematique, Vol. 361 (2023), 65--72. PDF
[13] Control theorems for fine Selmer groups, and duality of fine Selmer groups attached to modular forms (with Debanjana Kundu, Antonio Lei, and Jishnu Ray), The Ramanujan Journal, Vol. 60 (2023), 237-258. PDF
[12] Two infinite families of elliptic curves with rank greater than one (with Jason Stack), Integers, Vol. 22 (2022), #A1. PDF
[11] Λ-submodules of finite index of anticyclotomic plus and minus Selmer groups of elliptic curves (with Antonio Lei and Stefano Vigni), manuscripta mathematica, Vol. 167, No. 3-4 (2022), 589-612. PDF
[10] Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms -- Part II (with Antonio Lei), Journal of Number Theory, Vol. 229 (2021), 342-363. PDF
[9] Groups of generalized G-type and applications to torsion subgroups of rational elliptic curves over infinite extensions of Q (with Harris B. Daniels and Maarten Derickx), Transactions of the London Mathematical Society, Vol. 6, No. 1 (2019), 22-52. PDF, Magma Code
[8] Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms (with Antonio Lei), Mathematical Research Letters, Vol. 26, No. 4 (2019), 1115-1144. PDF
[7] Arithmetic properties of signed Selmer groups at nonordinary primes (with Antonio Lei), Annales de l'Institut Fourier, Vol. 69, No. 3 (2019), 1259-1294. PDF, Magma Code
[6] Rank parity for congruent supersingular elliptic curves, Proceedings of the AMS, Vol. 145 (2017), 3775-3786. PDF
[5] Modular forms of arbitrary even weight with no exceptional primes, Journal of Number Theory, Vol. 166 (2016), 158-165. PDF
[4] Elliptic curves with maximally disjoint division fields (with Harris B. Daniels and James Ricci), Acta Arithmetica, Vol. 175, No. 3 (2016), 211-223. PDF
[3] Obstruction criteria for modular deformation problems, International Journal of Number Theory, Vol. 12, No. 1 (2016), 273-285. PDF
[2] The Probability of Relatively Prime Polynomials in Zpk[x] (with Thomas R. Hagedorn), Involve, a Journal of Mathematics, Vol. 3, No. 2 (2010), 223-232. PDF
[1] Numerical Evidence on the Uniform Distribution of Power Residues for Elliptic Curves (with Amanda Hittson), Involve, a Journal of Mathematics, Vol. 2, No. 3 (2009), 305-321. PDF
[0] My PhD thesis, University of Massachusetts Amherst (2015)
Curriculum Vitae
Misc
Here are some notes I wrote for the Arithmetic Geometry at UNT 2025 workshop, discussing recent applications of the Iwasawa theory of elliptic curves to more mainstream problems in arithmetic geometry.
Some people seem to have enjoyed an introduction to the local-global principle that I wrote as an undergraduate.
Finally, here is my unpublished undergraduate senior thesis, which investigates the ranks that occur in a family of elliptic curves parameterized by twin primes.
Contact:
Mail:
Union College
Bailey Hall 202
Schenectady, NY 12308
Office: Bailey Hall 206A
Phone: 518-388-6163
E-mail:
haSPAMtleyj@un
REMOVETHISion.edu
Personal Zoom
Friends:
Adithya Chakravarthy
Michael Chou
Harris B. Daniels
Holley Friedlander
Rylan Gajek-Leonard
Alden Gassert
Asimina Hamakiotes
Hunter Handley
Keenan Kidwell
Debanjana Kundu
Antonio Lei
Álvaro Lozano-Robledo
Zachary Porat
Anwesh Ray
Hanson Smith
Sam Taylor
Stefano Vigni
Tom Weston
Glen Wilson
