Rational Points on Algebraic Varieties

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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.