Research

Elliptic Curves and Elliptic Divisibility Sequences

For my PhD thesis, I'm currently studying elliptic divisibility sequences and elliptic curves under the guidance of Kate Stange. We can define the addition of points of an elliptic curve geometrically. Under this addition law, the points of an elliptic curve form a group.  We can then define the multiplication by n map by [n]P = P + P + . . . + P where we add P to itself n times.

Elliptic divisibility sequences appear in the denominators of the sequence of rational points [n]P. I have been exploring these sequences modulo powers of primes, which has led me to using techniques from p-adic analysis, formal groups, and elliptic curves. 

Talks: 

"Limiting Density of Elliptic Divisibility Sequences," Canadian Mathematical Society Winter Meeting, November 29-December 2, 2024.

"Limiting Density of Elliptic Divisibility Sequences," West Coast Number Theory, December 15-19, 2024.

"Limiting Density of Elliptic Divisibility Sequences," Integers Conference, May 14-17, 2025.

"Limiting Density of Elliptic Divisibility Sequences," to be given at AMS Fall Southeastern Sectional Meeting, October 3-5, 2025.

"Elliptic Divisibility Sequences Modulo Powers of a Prime," to be given at AMS Fall Central Sectional Meeting, October 18-19, 2025.

Arithmetic Dynamics

I recently worked on dynamical irreducibility of polynomials on finite fields with Tori Day, Jamie Juul, Cigole Thomas, Bianca Thompson, and Bella Tobin. A polynomial is said to be dynamically irreducible if every iterate f(x), f(f(x)), f(f(f(x))), ... is irreducible. A unicritical polynomial is a polynomial with one critical point. We provide criteria for when a unicritical polynomial is dynamically irreducible over finite fields. We also explore dynamical irreducibility for cubic polynomials over finite fields. This project started at Rethinking Number Theory 4 (Summer 2023).

Preprint: "Dynamical Irreducibility of Certain Families of Polynomials over Finite Fields." With  Tori Day, Jamie Juul, Cigole Thomas, Bianca Thompson, and Bella Tobin. September 2024, arXiv.

Research Assistantships

Spring 2025

Spring 2023