Rylan Gajek-Leonard Visiting Assistant Professor Department of Mathematics Union College 807 Union St Schenectady NY 12308 Office: Bailey Hall 206B e-mail:  gajekler@union.edu CV

About me

I am currently a Visiting Assistant Professor at Union College in Schenectady, NY, where my research focuses on arithmetic geometry and algebraic number theory. Specifically, I am interested in the Iwasawa theory of elliptic curves and modular forms, p-adic L-functions, and Galois representations. Other interests include p-adic analysis and the Galois theory of certain families of polynomials.

I enjoy teaching all types of mathematics, from calculus to number theory. One of my main goals in the classroom is creating an inclusive space where students of all backgrounds can think deeply and creatively about mathematics.

Outside of academia, I enjoy playing the cello (you can listen to some old recordings here) and spending time with my dog, Ginny.

Publications

6. On the discriminants of truncated logarithmic polynomials,
   with J. Cullinan. Integers, accepted March 2025.


7. Stretching Newton polygons using pure polynomials,
   with U. Tomer.^* American Mathematical Monthly, accepted Jan. 2025.


8. A bound on the μ-invariants of supersingular elliptic curves,
   Canadian Mathematical Bulletin, accepted Jan. 2025.


9. Entanglement of elliptic curves upon base extension,
   with T. Day. International Journal of Number Theory, accepted Dec. 2024.


10. On a conjecture of Mazur predicting the growth of Mordell—Weil ranks in Z_p-extensions,
    with J. Hatley, D. Kundu, and A. Lei. Mathematical Research Letters, accepted Dec. 2024.


11. On the Newton polygons of Kaneko-Zagier lifts of supersingular polynomials,
    with J. Cullinan. Research in Number Theory, 2:34 (2016).


12. PhD thesis, University of Massachusetts Amherst (2022)

^*Undergraduate collaborator.

Preprints

• Iwasawa invariants of modular forms with a_p=0,
  submitted, 2023.

Miscellanea