Mathematical Sciences: Research Proposal on Arithmetic Geometry

柴 95-02186 柴教授将继续他的工作模空间的阿贝尔品种。特别是，他希望研究密度赫克轨道在某些志村品种。他还希望研究规范解除阿贝尔品种和某些类的动机。他希望应用他的结果来证明某些正则积分模型的存在性。 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。 此类代码对于现代计算机（硬盘）和光盘都是必不可少的。

Chai 95-02186 Professor Chai will continue his work on moduli spaces of Abelian varieties. In particular, he wishes to study the density of Hecke orbits in certain Shimura varieties. He also wishes to study the canonical lifting of Abelian varieties and certain classes of motives. He hopes to apply his results to prove the existence of certain canonical integral models. 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.