Mathematical Sciences: Galois Structure on Schemes & Capacity Theory on Varieties

钦伯格教授将致力于方案的伽罗瓦模结构的理论，以及容量理论和簇的交集理论之间的联系。特别是，他将致力于将算术交集理论推广到算术循环的极限。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 Chinburg will work on a theory for a Galois Module Structure for Schemes and the connection between capacity theory and intersection theory on varieties. In particular, he will work on generalizing arithmetic intersection theory to limits of arithmetic cycles. 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.