Research

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?

Published and Accepted Papers

1.  On the Acyclicity of Elliptic Curves Modulo Primes in Arithmetic Progressions; journal

   • Joint work with Nathan Jones 

   • Rev. Mat. Iberoam. Vo. 42, No. 3 (2026), 803 -- 830

2. Opposing Average Congruence Class Biases in the Cyclicity and Koblitz Conjectures for Elliptic Curves; journal

   • Joint work with Jacob Mayle and Tian Wang

   • Accepted in Canad. J. Math.

3.  On the Average Congruence Class Bias for Cyclicity and Divisibility of the Groups of F_p-points of Elliptic Curves; journal

   • J. Number Theory Vol. 278 (2026), 746 -- 785

Preprints

1.  On the Density of Coprime Reductions of Elliptic Curves; preprint

   • Joint work with Asimina S. Hamakiotes, Jacob Mayle, and Tian Wang

   • Submitted

2. Divisibility Biases in the Orders of Elliptic Curve Reductions; preprint

   • Joint work with Nara Sheen

   • Submitted

3. Average Twin Prime Conjecture for Elliptic Curves in Arithmetic Progressions; preprint

   • Joint work with Ahmet M. Güloğlu, Asimina S. Hamakiotes, and Tian Wang

In Preparation

1. Congruence Obstructions in the Refined Koblitz Conjecture

   • Joint work with Jacob Mayle and Rakvi

Thesis

• On the Distribution in Arithmetic Progressions of Primes of Various Properties Related to Elliptic Curves (Link)