Mathematical Sciences: Presidential Young Investigator Award

这位年轻的总统研究员将研究椭圆表面的Mordell-Weil格子，Tate-Safarevic群的大小和结构，以及通过Barnes-Wall格子与编码理论的联系。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。

This Presidential Young Investigator will work on Mordell- Weil lattices of elliptic surfaces, the size and structure of the Tate-Safarevic group and the connection to coding theory via the Barnes-Wall lattices. 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.