Mathematical Sciences: Trace Forms and Stickelberger Relations

莫拉莱斯教授将研究一般有限数域扩展中与整迹形式相关的不变量。他想看看在偶数度域中，与跟踪形式相关的类是否存在类似斯蒂克尔伯格的条件。这个项目属于算术几何的一般领域，它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。

Professor Morales will study invariants associated to integral trace forms in normal tame finite extensions of number fields. He wants to see whether there are Stickelberger like conditions for classes associated to trace forms in fields of even degree. 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.