# 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?

Preprints

On the Average Congruence Class Bias for Cyclicity and Divisibility of the Groups of Fp-points of Elliptic Curves; preprint (Link); Submitted

On the Acyclicity of Elliptic Curves Modulo Primes in Arithmetic Progressions; preprint (Link); Submitted

Joint work with Nathan Jones

In Preparation

Keywords: Drinfeld Modules; Cyclic Reduction

Decided to add more materials to the original manuscript. This will be available in late 2024.

Keywords: Refined Koblitz Conjecture, Serre's Cyclicity Problem, Arithmetic Progressions

Joint work with Jacob Mayle and Tian Wang.