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

About me

I am an Assistant Professor at Union College in Schenectady, NY, where my research focuses broadly on number theory and arithmetic geometry. More 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.

Preprints

• Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two,
  with A. Lei, 2025.

Publications

• Iwasawa invariants of modular forms with a_p=0,
  To appear in Annales de l’Institut Fourier.
• Stretching Newton polygons using pure polynomials,
  with U. Tomer.^* To appear in The American Mathematical Monthly.
• On a conjecture of Mazur predicting the growth of Mordell—Weil ranks in Z_p-extensions,
  with J. Hatley, D. Kundu, and A. Lei. To appear in Mathematical Research Letters.
4. On the discriminants of truncated logarithmic polynomials,
   with J. Cullinan. Integers, vol. 25, article 39 (2025).
5. A bound on the μ-invariants of supersingular elliptic curves,
   Canadian Mathematical Bulletin, vol. 68, no. 3, pp. 787-796 (2025)
6. Entanglement of elliptic curves upon base extension,
   with T. Day. International Journal of Number Theory, vol. 21, no. 6, pp. 1297-1315 (2025).
7. On the Newton polygons of Kaneko-Zagier lifts of supersingular polynomials,
   with J. Cullinan. Research in Number Theory, vol. 2, article 34 (2016).
8. PhD thesis, University of Massachusetts Amherst (2022).

^*Undergraduate collaborator.