Mathematical Sciences: Galois Representations Occurring in Mordell-Weil Groups

Rohrlich教授将研究几个问题， 随着Mordell-Weil的伽罗瓦表示的实现， 椭圆曲线群 特别是，某些 不可约的阿廷表示出现，如果是这样，它们是什么 多样性 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 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.