Rational Points on Algebraic Varieties

My research centres on the distribution of rational points on algebraic varieties. In particular, I have proved and am aiming to prove results concerning the abundance and distribution of rational points on algebraic surfaces.

Most of my research so far has focused on the Hilbert property, a geometric notion of the abundance of rational points on algebraic varieties with links to Zariski-density, weak weak approximation and the inverse Galois problem. My primary tool has been the theory of fibrations.

During my first semester, I worked on proving the Hilbert property is satisfied for a certain class of double elliptic surfaces, namely diagonal quartic surfaces with certain coefficient conditions. Unfortunately, results which I hoped to prove were published during this time, but I gained a good deal of knowledge in the general theory of rational points and fibrations which I later applied in my research.