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?

List of Publications

1.  In Preparation (Keywords: Drinfeld Modules, Cyclic Reduction)

   • Decided to add more materials to the original manuscript. This will be available in Summer, 2024.

2.  In Preparation (Keywords: Refined Koblitz Conjecture, Serre's Cyclicity Problem, Arithmetic Progressions)

   • Joint work with Jacob Mayle and Tian Wang

3.  On the average congruence class bias for cyclicity and divisibility of the groups of Fp-points of elliptic curves; preprint (Link)

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

   • Joint work with Nathan Jones