Mathematical Sciences: Arithmetic Geometry

米尔恩教授将研究志村品种。 他希望 将Shimura品种的接合结果扩展到 混合志村品种;扩展的猜想证明， Langlands和Rapapport从志村品种的PEL型， 其他志村品种。 他还希望看到， 由动机定义的属性。 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 Milne will work on Shimura varieties. He hopes to extend the results on the conjugation of Shimura varieties to mixed Shimura varieties; to extend the proof of the conjecture of Langlands and Rapapport from Shimura varieties of PEL-type to other Shimura varieties. He also hopes to see whether the properties conjecturally defined by motives hold. 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.