Rational Points on Algebraic Varieties

我的研究集中在代数簇上有理点的分布上。特别是，我已经证明，并旨在证明有关结果的丰度和分布的合理点的代数surface.Most我的研究迄今为止一直集中在希尔伯特财产，一个几何概念的丰度合理点的代数簇与链接Zerkiki-密度，弱弱逼近和逆伽罗瓦问题。我的主要工具是纤维化理论。在我的第一个学期，我致力于证明希尔伯特性质是满足一定的一类双椭圆曲面，即对角四次曲面与某些系数条件。不幸的是，结果，我希望证明发表在这段时间内，但我获得了大量的知识，一般理论的合理点和纤维化，我后来应用在我的研究。

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.