Mathematical Sciences: RUI: Arithmetic of Modular Forms and Algebraic Varieties

Gouvea教授将致力于与p-进模形式理论相关的几个问题。特别是，他将研究关于由同余条件连接的模形式的存在的猜想。他还将研究扭族中椭圆曲线的算术性质。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 Gouvea will work on several problems connected with the theory of p-adic modular forms. In particular, he will study conjectures on the existence of modular forms connected by congruence conditions. He will also work on the arithmetic properties of elliptic curves in twisted families. 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.