Mathematical Sciences: Formal Groups and Igusa Curves

基廷教授将致力于研究模曲线理论中出现的伊古萨塔，它是定义在形变的模空间上的某些形式群的自同构群的作用，最后刻画由形变得到的形式群所产生的场。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 Keating will work on the Igusa tower that arise in the theory of modular curves, the action of the automorphism group of certain formal groups defined on the moduli space of deformations and finally to characterize the fields arising from formal groups obtained by deformations. 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.