Mathematical Sciences: On the p-adic Geometry of Modular Curves

9307195科尔曼教授将继续他在刚性分析方面的工作，特别是将这些技术应用于模数曲线。他希望在附加到模形式的表示的素数p处获得关于局部行为的信息。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。***

9307195 Coleman Professor Coleman will continue his work on rigid analysis in particular to applying these techniques to modular curves. He hopes to obtain information about he local behavior at a prime p of the representations attached to a modular form. 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. ***