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

9307195科尔曼 教授科尔曼将继续他的工作刚性分析，特别是应用这些技术的模块化曲线。他希望获得有关附加到模形式的表示在素数p处的局部行为的信息。 这个项目福尔斯属于算术几何的一般领域-一个融合了两个最古老的数学领域：数论和几何的主题。 事实证明，这种结合非常富有成效--最近解决了几代人都无法解决的问题。 在它的许多后果是新的纠错码。 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. ***