My primary research interest lies in Arithmetic Geometry, a field of research where geometry and number theory meet. Most of my research questions can be reduced to a following statement;
Let E be an elliptic curve over Q. Let p be a prime of good reduction, and hence E_p is an elliptic curve over F_p. Consider a geometric property P an elliptic curve over a finite field can satisfy. Consider; given E/Q, how many primes are there that make E_p satisfy the property P? If there are infinite, what is the density of such primes?
Papers
On the Acyclicity of Elliptic Curves Modulo Primes in Arithmetic Progressions; preprint (Link); Submitted
Joint work with Nathan Jones
Accepted in Rev. Mat. Iberoam.
Opposing Average Congruence Class Biases in the Cyclicity and Koblitz Conjectures for Elliptic Curves; preprint (Link)
Joint work with Jacob Mayle and Tian Wang
Accepted in Canad. J. Math.
On the Average Congruence Class Bias for Cyclicity and Divisibility of the Groups of Fp-points of Elliptic Curves; preprint (Link); Submitted
J. Number Theory Vol. 278 (2026), 746 -- 785
Thesis
On the Distribution in Arithmetic Progressions of Primes of Various Properties Related to Elliptic Curves (Link)