## Rylan Gajek-LeonardVisiting Assistant ProfessorDepartment of Mathematics Union College 807 Union St Schenectady NY 12308 Office: Bailey Hall 108B e-mail:
gajekler@union.edu
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I am interested in algebraic number theory and arithmetic geometry. My current research is in the Iwasawa theory of elliptic curves and modular forms. I am especially interested in understanding the behavior of p-adic L-functions attached to nonordinary modular forms.

*Stretching Newton polygons using pure polynomials,*

with U. Tomer. Submitted, 2024.*Entanglement of elliptic curves upon base extension,*

with T. Day. Submitted, 2024.*On a conjecture of Mazur predicting the growth of Mordellâ€”Weil ranks in Z*_{p}-extensions,

with J. Hatley, D. Kundu, and A. Lei. Submitted, 2024.*On the discriminants of truncated logarithmic polynomials,*

with J. Cullinan. Submitted, 2023.*Iwasawa invariants of modular forms with a*_{p}=0,

submitted, 2023.*On the Newton polygons of Kaneko-Zagier lifts of supersingular polynomials,*
with J. Cullinan. Research in Number Theory, 2:34 (2016).

I am currently a visiting assistant professor at Union College in Schenectady, NY. 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.

I also play the cello.