Curriculum Vitae

• Education

  • University of Massachusetts, Amherst, MA
    • Ph.D. in Mathematics, 2015
    • Thesis advisor: Tom Weston
  • University of Massachusetts, Amherst, MA
    • M.S. in Mathematics, 2011
  • The College of New Jersey, Ewing, NJ
    • B.A. in Mathematics with honors, 2009
    • Minor: Art History; Phi Beta Kappa

• Employment

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

• Publications

  • [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 2^mp, 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 Z_p-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 F_p[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.
  • [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 Z_p^k[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

• Union College, Fall 2015 - Present
  • Calculus I, Calculus II, and Multivariable Calculus with Linear Algebra
  • Introduction to Logic and Set Theory
  • Number Theory
  • Real Variable Theory
  • Complex Analysis
  • Mathematical Cryptology
  • Ordinary Differential Equations
  • Differential Equations
  • Applied Linear Algebra
  • Independent Studies:
  • Algebraic number theory
  • p-adic Numbers
  • Galois theory
  • Commutative algebra
  • A sample of advised senior theses
  • Frank Rocco, Elliptic Curve Cryptology (2017)
  • Casey Bruck, A Concrete Example of Prime Behavior in Quadratic Fields (2017)
  • Allegra Dawes, Geometric Group Theory and Hyperbolic Groups (2019)
  • Nicholas Kender, Symmetric Polynomials: The Fundamental Theorem and Uniqueness (2019)
  • Edward Winters, Analysis of the Doomsday Algorithm (2020)
  • Zachary Porat, Classification of Torsion Subgroups for Mordell Curves (2020)
  • Thomas Farina, The Relationship Between Zeros of the Riemann Zeta Function and Primes (2021)
  • Daniel Tyebkhan, Factoring Integers with Elliptic Curves (2023)
  • Khai Dong, Attacks on Discrete-Log Cryptography on Elliptic Curves (2024)
  • Mayah Teplitskiy, Elliptic Curves and Diophantine Stability (2024)
  • Olivia Riley, The Fundamental Theorem of Algebra: A Linear Algebraic Approach (2025)
  • Jacob Shuckman, Schemes: Spaces for Algebraic Geometry (2025)
• University of Massachusetts, Amherst, Fall 2009 - Spring 2015
  • Calculus I, Calculus II, and Calculus II for Life Sciences and Business
  • Linear Algebra

• Mentorship and Outreach

  Rethinking Number TheoryVirtual

  Project Leader (with Zachary Porat)June 22 - July 3, 2026
  Arithmetic Geometry at UNT 2025Denton, TX

  Lecturer and Project LeaderMay 5 - 9, 2025
  Undergraduate Research AdvisedSchenectady, NY

  • Mayah Teplitskiy, Polynomials over fields of characteristic p which commute under composition (Winter 2022-Spring 2022); See Publication #15
  • Jason Stack, Infinite families of elliptic curves of large rank (Fall 2021); See Publication #12
  • Jason Stack and Tzu-Ruei Huang, Noncongruence witnesses for elliptic curves (Summer 2020)
  • Casey Bruck, Composite Sequences and Covering Systems (Summer 2017)

• Recent and Upcoming Invited/Plenary Talks

  Amherst CollegeAmherst, MA

  Five College Number Theory SeminarApril 28, 2026
  California State University San MarcosSan Marcos, CA

  San Marcos Informal Mathematics In-Person ColloquiumNovember 20, 2025
  CUNY Graduate CenterNew York, NY

  Arithmetic Geometry SeminarOctober 21, 2025
  University of North TexasDenton, TX

  Arithmetic Geometry at UNT 2025May 5-9, 2025
  AMS Sectional MeetingSan Luis Obispo, CA

  Special Session: Number theory at PUIsMay 3, 2025
  University of Texas Rio Grande ValleyEdinburg, TX

  Algebra and Number Theory SeminarApril 15, 2025
  University of OttawaOttawa, Canada

  Mathematics ColloquiumNovember 13, 2024
  University of OttawaOttawa, Canada

  Ottawa/Carleton Number Theory SeminarNovember 11, 2024
  West Chester UniversityWest Chester, PA

  Mathematics ColloquiumMarch 20, 2024
  Joint Mathematics MeetingsBoston, MA

  AMS Special Session: Number Theory at Non-PhD Granting InstitutionsJanuary 5, 2023
  AMS Sectional MeetingAmherst, MA

  Special Session: Algebraic and Analytic Theory of Elliptic CurvesOctober 2, 2022
  AMS Sectional MeetingAmherst, MA

  Special Session: Iwasawa TheoryOctober 1, 2022
  Amherst CollegeAmherst, MA

  Five College Number Theory SeminarMarch 8, 2022
  Canadian Mathematical Society Summer MeetingOnline (Zoom)

  Scientific session: Algebraic number theoryJune 8, 2021
  Joint Mathematics MeetingsOnline (Zoom)

  AMS Special Session: A Showcase of Number Theory at Undergraduate InstitutionsJanuary 6, 2021
  Arizona State UniversityOnline (Zoom)

  Number Theory Seminar: Iwasawa theory in the positive rank settingNovember 20, 2020
  University of VermontBurlington, VT

  unQVNTSOctober 31, 2019
  The College of New JerseyEwing, NJ

  Mathematics ColloquiumSeptember 25, 2019
  University of ColoradoBoulder, CO

  Front Range Number Theory DayApril 27, 2019
  AMS Sectional MeetingHartford, CT

  Special Session: Algebraic number theoryApril 14, 2019
  Cornell UniversityIthaca, NY

  Number Theory SeminarNovember 16, 2018
  Joint Mathematics MeetingsSan Diego, CA

  MAA Special Session: Innovative Teaching PracticesJanuary 11, 2018
  Amherst CollegeAmherst, MA

  Five College Number Theory SeminarDecember 5, 2017
  University of ConnecticutStorrs, CT

  Algebra SeminarNovember 1, 2017
  Université LavalQuébec City, Canada

  Séminaire d'algèbre et de géométrieMarch 7, 2016
  Amherst CollegeAmherst, MA

  Five College Number Theory SeminarFebruary 9, 2016

• Recent Contributed Talks

  Université LavalQuébec City, Canada

  CNTA XVJuly 11, 2018
  University of ConnecticutStorrs, CT

  CTNT 2018June 1, 2018
  University of BuffaloBuffalo, NY

  Upstate New York Number Theory ConferenceApril 29, 2018
  Joint Mathematics MeetingsSan Diego, CA

  AMS Special Session: Number Theory IJanuary 10, 2018
  Binghamton UniversityBinghamton, NY

  Upstate New York Number Theory ConferenceMay 6, 2017
  Joint Mathematics MeetingsAtlanta, GA

  AMS Contributed Paper Session: Number theory IJanuary 4, 2017
  Laval UniversityQuébec City, Canada

  Maine/Québec Number Theory ConferenceOctober 8, 2016

• Grants

• 2024-2027 AMS-Simons Research Enhancement Grant for PUI Faculty
• 2024-2025 Union College Faculty Research Fund
• 2025-2027 NSF Collaborative grant DMS-2429253 Hudson River Undergraduate Mathematics Conference (collaborative with Kariane Calta, Paul Friedman, and Greg Malen)
• 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

  • Departmental server sysadmin (Fall 2022 - present)
  • Curriculum Steering Committee (Fall 2021 - present)
  • Co-organizer for Student Seminar, Union College (Winter-Spring 2017; Spring 2022 - Winter 2023; Spring 2026 - Present)
  • Departmental website co-editor (Winter 2019- present)
  • REU liason, Union College (Fall 2015 - present)
  • Admissions co-liason (Fall 2018 - Spring 2020)
  • Graduate school liason, Union College (Fall 2015 - Spring 2018)
  • Co-organizer of the 2016 and 2019 Union College Math Conferences

• Union College Service

  • AAC Subcouncil for Academic Integrity, Division III representative (Winter 2026 - present)
  • Educating Character Initiative, Leadership team (Fall 2026 -- Present)
  • Factuly Appeals Committee, Chair alternate (Fall 2026 -- Present)
  • Liaison Committee on Study Abroad, Division III substitute representative (Spring 2026)
  • Faculty Review Board, Division III substitute representative (Winter 2026)
  • Committee on Student Standing, substitute representative (Spring 2025 and Fall 2025)
  • Facult Appeals Committee (Fall 2023 - Spring 2025)
  • 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:

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