Mathematical Sciences: Arithmetic Geometry

柴教授谈算术几何中的几个问题。其中包括Shimura簇的正则积分模型和p-进对称空间的理论，以期类似于关于Hodge结构退化的Schmidt定理。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 Chai on several problems in arithmetic geometry. These include canonical integral models of Shimura varieties and the theory of p-adic symmetric spaces with a view to an analogue of Schmidt's theorem on degenerations of Hodge structures. 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.