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 of Mathematics 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.

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. You can find a list of courses that I've taught here.

I received my PhD from the University of Massachusetts Amherst under the supervision of Tom Weston. Before that, I completed Part III of the Mathematical Tripos (MASt) at the University of Cambridge, where I also performed regularly as assistant principal cello with the Cambridge Philharmonic. My undergraduate studies were at Bard College and the Bard College Conservatory, where I completed a double degree in mathematics and cello performance. I am a Canadian citizen and grew up on Salt Spring Island, British Columbia.

Outside of mathematics, some things that I enjoy are:

• Playing the cello
• Spending time with my dog
• Gardening

Publications and preprints

• A canonical construction of signed p-adic L-functions for non-ordinary modular forms of weight ≤ p+1, (arXiv)
  with A. Lei. Preprint.

8. Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two, (journal | arXiv)
   with A. Lei. Advances in Mathematics, vol. 502, part B, article 111141 (2026).
9. Iwasawa invariants of modular forms with a_p=0, (arXiv)
   To appear in Annales de l’Institut Fourier.
10. Stretching Newton polygons using pure polynomials, (journal | arXiv)
    with U. Tomer.^* The American Mathematical Monthly, vol. 133, issue 6 (2026), pp. 532–539.
11. On a conjecture of Mazur predicting the growth of Mordell—Weil ranks in Z_p-extensions, (journal | arXiv)
    with J. Hatley, D. Kundu, and A. Lei. Mathematical Research Letters, vol. 32, issue 6 (2025), pp. 1877–1912.
12. On the discriminants of truncated logarithmic polynomials, (journal)
    with J. Cullinan. Integers, vol. 25, article 39 (2025).
13. A bound on the μ-invariants of supersingular elliptic curves, (journal | arXiv)
    Canadian Mathematical Bulletin, vol. 68, no. 3 (2025), pp. 787–796.
14. Entanglement of elliptic curves upon base extension, (journal | arXiv)
    with T. Day. International Journal of Number Theory, vol. 21, no. 6 (2025), pp. 1297–1315.
15. On the Newton polygons of Kaneko-Zagier lifts of supersingular polynomials, (journal)
    with J. Cullinan. Research in Number Theory, vol. 2, article 34 (2016).
16. PhD thesis, University of Massachusetts Amherst (2022).

^*Undergraduate collaborator.

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