Mathematical Sciences: Arthmetic of Elliptic Curves and Automorphic Forms over Function Fields

乌尔默教授将致力于函数域上椭圆曲线和自同构形的算术。特别地，他打算致力于Mazur猜想的类似工作，该猜想断言定义在有限域上的函数域上的椭圆曲线上的有理点群在某一ZP扩张上是有限生成的。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 Ulmer will work on the arithmetic of elliptic curves and automorphic forms over function fields. In particular, he intends to work on analogues of the conjecture of Mazur that asserts that the group of rational points on an elliptic curve defined over a function field over a finite field in a certain Zp extension is finitely generated. 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.