Mathematical Sciences: The Arithmetic of Curves of Genus Two

格兰特教授将研究二属曲线的算术的各个方面。他将研究这些曲线上的整数点，由2属曲线产生的某些单位，以及计算这些曲线的莫德尔-韦尔秩的新方法。这个项目属于算术几何的一般领域，这门学科融合了数学中两个最古老的领域：数论和几何。事实证明，这一组合非常富有成效——最近解决了几代人经受住了考验的问题。其诸多后果之一是新的纠错码。这些代码对现代计算机（硬盘）和光盘都是必不可少的。

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.