Mathematical Sciences: Arithmetic Algebraic Geometry

这笔赠款支持W.McCallum和D.Ulmer从事算术几何的研究。麦卡勒姆教授将研究费马曲线上的下降。乌尔默教授将研究模形式系数的p-进赋值以及椭圆曲线的岩泽理论。这个项目属于算术几何的一般领域--一个融合了数论和几何这两个最古老的数学领域的学科。事实证明，这种结合非常有成效--最近解决了几代人经受住的问题。在其众多后果中，有一种是新的纠错码。这种代码对于现代计算机(硬盘)和光盘都是必不可少的。

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.