Mathematical Sciences: The Arithmetic of Curves of Genus Two

格兰特教授将研究数学的各个方面 亏格为2的曲线 他将研究这些整数点 曲线，由亏格2的曲线产生的某些单位，以及新的 计算这种曲线的Mordell-Weil秩的方法。 这个项目福尔斯属于算术的一般范畴 几何学-一个融合了两个最古老的领域的主题， 数学：数论和几何。 这种组合有 被证明是非常富有成效的-最近解决了一些问题 经受住了几代人的考验 在其众多后果中， 纠错码 这些准则对现代和 计算机（硬盘）和光盘。

Professor Grant will work on various aspects of the arithmetic of curves of genus two. He will study integer points on these curves, certain units arising from curves of genus two, and new methods for calculating the Mordell-Weil rank of such curves. This project falls into the general area of arithmetic geometry -a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.