Mathematical Sciences: Capacity Theory on Varieties

鲁梅利教授将致力于阿德利克的部门容量研究 任意维数的射影簇上的集合。 他将 开发截面容量的特性，并试图证明 齐次形式猜想，在各种尺寸d， 截面容量由齐次形式的度决定 d+1。 这个项目福尔斯属于算术的一般范畴 几何学-一个融合了两个最古老的领域的主题， 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 Rumely will work on sectional capacity for adelic sets on projective varieties of arbitrary dimensions. He will develop properties of sectional capacity and attempt to prove the homogeneous form conjecture that on a variety of dimension d, the sectional capacity is determined by a homogeneous form of degree d+1. 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.