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

Hida教授将研究p进Hecke代数理论及其在CM场的Iwasawa理论中的应用。他还将研究全实场上的半积分权的形式，p进对称方形L-函数的构造及其在这些场的分圈Z-p塔中的应用。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。

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.