Mathematical Sciences: Theory of P-adic Hecke Algebras and Iwasawa Theory for CM Fields

希达教授将致力于p-adic Hecke理论 代数及其在CM域的岩泽理论中的应用 他 还将致力于研究半整数权重的形式， 全真实的域，p-adic对称方L- 函数及其在分圆Z-p塔上的应用 这些领域 这个项目福尔斯属于算术的一般范畴 几何学-一个融合了两个最古老的领域的主题， 数学：数论和几何。 这种组合有 被证明是非常富有成效的-最近解决了一些问题 经受住了几代人的考验 在其众多后果中， 纠错码 这些准则对现代和 计算机（硬盘）和光盘。

Professor Hida will work on the theory of p-adic Hecke algebras and their applications to Iwasawa theory of CM fields. He will also work on studying forms of half integral weight over totally real fields, the construction of p-adic symmetric square L- functions and their application to the cyclotomic Z-p tower of these fields. 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.