## 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

- [18]
*On a conjecture of Mazur predicting the growth of Mordell—Weil ranks in*(with Rylan Gajek-Leonard, Debanjana Kundu, and Antonio Lei), preprint. arXiv:2401.07792**Z**_{p}-extensions - [17]
*Statistics for anticyclotomic Iwasawa invariants of elliptic curves*(with Debanjana Kundu and Anwesh Ray),**Mathematische Zeitschrift**, Vol. 407, 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*(with Mayah Teplitskiy), to appear in**F**_{p}[x] which commute under composition**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**_{pk}[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

- [18]
## 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) - Directed undergraduate research
- Casey Bruck,
*Composite Sequences and Covering Systems*(2017) - Jason Stack and Tzu-Ruei Huang,
*Noncongruence witnesses for elliptic curves*(2020) - Jason Stack,
*Infinite families of elliptic curves of large rank*(2021); See Publication #12 - Mayah Teplitskiy,
*Polynomials over fields of characteristic*(Winter 2022-Spring 2022); See Publication #15*p*which commute under composition}

**University of Massachusetts, Amherst**, Fall 2009 - Spring 2015- Calculus I, Calculus II, and Calculus II for Life Sciences and Business
- Linear Algebra

## 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*, 2020. Université Laval*L**p*-adique d'une forme modulaire - 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

**Mail:
** Union College

Bailey Hall 202

Schenectady, NY 12308

haSPAMtleyj@un REMOVETHISion.edu

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