Mathematical Sciences: Arithmetic Algebraic Geometry

该基金支持W. McCallum和D. Ulmer 学习算术几何麦卡勒姆教授将研究 费马曲线的下降乌尔默教授将研究p-adic 模形式系数的赋值以及 椭圆曲线的岩泽理论。 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。

This grant supports the research of W. McCallum and D. Ulmer to work in arithmetic geometry. Professor McCallum will study descent on Fermat's curve. Professor Ulmer will study the p-adic valuations of coefficients of modular forms as well as the Iwasawa theory for elliptic 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.