Mathematical Sciences: Problems in Arithmetic Geometry and Complexity Theory

泰特尔鲍姆教授将致力于模曲线的p-进解析理论及其算术含义。他将学习模形式的高次权不变量，Shimura变种的算法和Drinfeld模曲线的算法。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。

Professor Teitelbaum will work on the p-adic analytic theory of modular curves and its arithmetic implications. He will study higher weight invariants of modular forms, the arithmetic of Shimura varieties and the arithmetic of Drinfeld modular 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.