Abelian Motives and Shimura Varieties

9622770米尔恩教授研究算术几何，特别是丢番图几何的问题。他将研究有限域上Shimura变分上点的Langlands猜想和Rapaport猜想。他还希望研究阿贝尔动机的退化，并希望利用与志村变的关系来获得志村变在数域上的紧化信息。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。?？

9622770 Milne Professor Milne works in arithmetic geometry specifically on problems in Diophantine geometry. He will study the conjecture of Langlands and Rapaport on points on Shimura varieties over finite fields. He also hopes to study the degeneration of abelian motives with the hope of exploiting the relation to Shimura varieties in order to obtain information about the compactifications of Shimura varieties over number 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. ??