Arithmetical Algebraic Geometry

该奖项为模形式，阿贝尔 变种和伽罗瓦表示Gerhard Frey的构造将整数的三元组与有理数上的椭圆曲线联系在一起，导致了研究者的主题与涉及整数的简单问题之间的直接联系。弗雷的构造导致了费马大定理的证明和数学中几个相关问题的解决。许多问题仍有待解决-ABC猜想可能是最有名的。人们预计，算术代数几何将继续蓬勃发展;调查人员正在研究的一些问题，现在“在桌子上”以及其他问题出现的时间。 这个项目福尔斯属于算术几何的一般领域-一个融合了两个最古老的数学领域：数论和几何的主题。 事实证明，这种结合非常富有成效--最近解决了几代人都无法解决的问题。 在它的许多后果是新的纠错码。 这种代码对于现代计算机（硬盘）和光盘都是必不可少的。

This award provides funds for studies of modular forms, abelian varieties, and Galois representations. Gerhard Frey's construction, which associates triples of integers to elliptic curves over the rational numbers, has led to a direct link between the investigator's subject and simple problems involving whole numbers. Frey's construction has led to a proof of Fermat's Last Theorem and a resolution of several allied problems in mathematics. Many questions remain to be resolved - the ABC conjecture is perhaps the best known. One expects that arithmetic algebraic geometry will continue to flourish; the investigator is working on some of the problems that are now "on the table" as well as other problems which emerge over time. 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.