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?


In Preparation