Jeffrey Hatley


Associate Professor
Department of Mathematics
Union College




Curriculum Vitae

  • Education

  • Employment

    • Union College, Schenectady, NY
      • Associate Professor, September 2023 - Present
      • Assistant Professor, September 2018 - August 2023
      • Visiting Assistant Professor, September 2015 - August 2018

  • Publications

    • [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), preprint. arXiv:2401.07792
    • [17] Statistics for anticyclotomic Iwasawa invariants of elliptic curves (with Debanjana Kundu and Anwesh Ray), preprint. arXiv:2106.01517
    • [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), to appear in 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.
    • [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
    • [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

  • Teaching Experience

  • Recent Invited Talks

    • ``Rational points on elliptic curves over (infinite) extensions,'' West Chester University Math Colloquium, March 20, 2024.
    • ``λ-invariant stability in families of modular Galois representations,'' AMS Special Session on Number Theory at Non-PhD Granting Institutions, Joint Math Meetings, January 5, 2023.
    • ``Arithmetic statistics for Iwasawa invariants of elliptic curves,'' AMS Sectional Meeting Special Session on Algebraic and Analytic Theory of Elliptic Curves (Amherst MA), October 2, 2022.
    • ``λ-invariant stability in families of modular Galois representations,'' AMS Sectional Meeting Special Session on Iwasawa Theory (Amherst MA), October 1, 2022.
    • "Arithmetic Statistics for Iwasawa Invariants of Elliptic Curves," Five College Number Theory Seminar, March 8, 2022.
    • "Recent progress in positive rank Iwasawa theory," Special session on algebraic number theory, Canadian Mathematical Society Summer Meeting, June 8, 2021.
    • "Comparing positive rank Iwasawa modules," AMS Special Session on A Showcase of Number Theory at Undergraduate Institutions, Joint Math Meetings, January 6, 2021.
    • "Iwasawa theory in the positive rank setting," Arizona State University Number Theory Seminar, November 20, 2020.
    • "Iwasawa Theory and Goldfeld's Conjecture", unQVNTS (University of Vermont), October 31, 2019.
    • "The Birch and Swinnerton-Dyer Conjecture," The College of New Jersey Mathematics Colloquium, September 25, 2019.
    • "Variation of arithmetic invariants in families," Front Range Number Theory Day (CU Boulder), April 27, 2019.
    • "Torsion subgroups of rational elliptic curves over infinite extensions," AMS Sectional Meeting Special Session on Algebraic Number Theory (Hartford CT), April 14, 2019.
    • "Anticyclotomic Iwasawa Theory in the Positive Rank Setting", Cornell University Number Theory Seminar, November 16, 2018.
    • "Heads or tails? Coin-flipping with elementary number theory," MAA Session on Innovative Teaching Practices in Number Theory, Joint Math Meetings 2018.
    • "Anticyclotomic Iwasawa theory in the positive corank case," Five College Number Theory Seminar, December 5, 2017
    • "Rank parity in families of nonordinary modular forms," University of Connecticut Algebra Seminar, November 1, 2017
    • "Unobstructed Modular Deformation Theory," Université Laval séminaire d'algèbre et de géométrie gradué, March 7, 2016
    • "Pairs of Elliptic Curves with Large Galois Image," Five College Number Theory Seminar, February 9, 2016.

  • Recent Contributed Talks

    • "Torsion subgroups of rational elliptic curves over infinite extensions," CNTA XV at Université Laval, July 11, 2018.
    • "Comparing Selmer groups of positive corank," CTNT 2018 at the University of Connecticut Storrs, June 1, 2018.
    • "Comparing Selmer groups of positive corank," Upstate New York Number Theory Conference, April 29, 2018.
    • "Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms," AMS Session on Number Theory I, Joint Math Meetings 2018.
    • "Rank parity for congruent modular forms," Upstate New York Number Theory Conference, May 6, 2017
    • "Arithmetic properties of signed Selmer groups at nonordinary primes," Joint Math Meetings 2017
    • "Rank parity for congruent supersingular elliptic curves," Conférence de Théorie des Nombres Québec-Maine, October 8, 2016
    • "Elliptic curves with maximally disjoint division fields," Maine-Québec Number Theory Conference, October 3, 2015

  • Grants

    • 2019-2022 NSF Collaborative grant. DMS-1901866 Upstate New York Number Theory Conference (collaborative with Ravi Ramakrishna and Doug Haessig)

  • Professional Service

    • Referee for Transactions of the AMS, Proceedings of the LMS, Bulletin of the LMS, Annales mathématiques du Québec, the International Journal of Number Theory, Rad HAZU, and American Mathematical Monthly
    • Author of Mathematical Reviews for MathSciNet
    • Master's thesis committee for Cédric Dion, Fonction L p-adique d'une forme modulaire, 2020. Université Laval
    • Undergraduate Poster Judge at JMM 2021
    • Local Organizer: Upstate Number Theory Conference 2021

  • Departmental Service

    • Curriculum Committee (Fall 2021 - Present)
    • Admissions co-liason (Fall 2018 - Spring 2020)
    • Graduate school liason, Union College (Fall 2015 - Spring 2018)
    • REU liason, Union College (Fall 2015 - Present)
    • Departmental website co-editor (Winter 2019- Present)
    • Co-organizer of the 2016 and 2019 Union College Math Conferences
    • Co-organizer for Student Seminar, Union College (Winter-Spring 2017)

  • Union College Service

    • Faculty Review Board, Center 2 non-tenured representative (Fall 2021 - Spring 2022)
    • Undergraduate Research Committee Division III representative (Winter 2019 - Present)
    • Writing Board Division III representative (Winter 2019)
    • Ad hoc tenure committee (Fall 2023)

  • Honors and Awards

    • Departmental Distinguished PhD Thesis Award, UMass Amherst, 2015
    • Phi Beta Kappa Membership, Delta of New Jersey, 2009

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:

Michael Chou
Harris B. Daniels
Holley Friedlander
Rylan Gajek-Leonard
Alden Gassert
Keenan Kidwell
Debanjana Kundu
Antonio Lei
Álvaro Lozano-Robledo
Zachary Porat
Anwesh Ray
Hanson Smith
Sam Taylor
Stefano Vigni
Tom Weston
Glen Wilson