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

Gouvea教授将研究几个问题， p-adic模形式的理论。 特别是，他将 连接的模形式存在性的研究 一致性条件 他还将致力于算术 扭族中椭圆曲线的性质 这个项目福尔斯属于算术的一般范畴 几何--一门融合了几何学两个最古老领域的学科 数学：数论和几何。 这种组合有 被证明是非常富有成效的-最近解决了一些问题 经受住了几代人的考验 在其众多后果中， 纠错码 这些准则对现代和 计算机（硬盘）和光盘。

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.