Mathematical Sciences: Galois Representations Occurring in Mordell-Weil Groups

Rohrlich教授将致力于与椭圆曲线的Mordell-Weil群的Galois表示的实现有关的几个问题。具体地说，是否存在某些不可约的Artin表示，如果是，它们的多重性是什么。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 Rohrlich will work on several problems connected with the realization of Galois representations of Mordell-Weil groups of elliptic curves. In particular, whether certain irreducible Artin representations occur and if so what are their multiplicities. 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.