Mathematical Sciences: Refined Conjectures of Birch and Swinnerton-Dyer Type, and Regular Algebras

泰特教授将研究伯奇和斯温纳顿-戴尔类型的精细猜想。特别是，他将研究这一猜想的几何类比及其与二维类场论的可能联系。他还将研究大于3维的正则分级结合代数。这个项目属于算术几何的一般领域，这门学科融合了数学中两个最古老的领域：数论和几何。事实证明，这一组合非常富有成效——最近解决了几代人经受住了考验的问题。其诸多后果之一是新的纠错码。这些代码对现代计算机（硬盘）和光盘都是必不可少的。

Professor Tate will work on refined conjectures of Birch and Swinnerton-Dyer type. In particular, he will study a geometric analogue of this conjecture and its possible connections with two dimensional class field theory. He will also study regular graded associative algebras in dimensions greater than three. 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.