Mathematical Sciences: Arithmetic Geometry

米尔恩教授将研究志村品种。他希望将志村变种共轭的结果推广到混合志村变种；将Langlands和Rapapport猜想的证明从pel型的志村变种推广到其他志村变种。他还希望看到由动机推测定义的属性是否成立。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 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.