Mathematical Sciences: Trace Forms and Stickelberger Relations

莫拉莱斯教授将研究数域的正规驯服有限扩张中与积分迹形式有关的不变量。他想知道偶数度域中与迹形式相关的类是否存在与Stickelberger类似的条件。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 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.