Mathematical Sciences: Arithmetic Algebraic Geometry

该基金支持W. McCallum和D. Ulmer在算术几何方面的研究。麦卡勒姆教授将研究费马曲线的下降。Ulmer教授将研究模形式系数的p进值以及椭圆曲线的Iwasawa理论。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。

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.