Mathematical Sciences: Shimura Varieties and Abelian Varieties

Silverberg教授将继续她对志村变种的研究。特别是，她计划研究有界对称域的算术商的正则模型上点的共轭表示。她还打算研究阿贝尔变种上由相邻扭转点获得的场的问题。这个项目属于算术几何的一般领域，它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 Silverberg will continue her work on Shimura varieties. In particular, she plans to study adelic representations attached to points on canonical models of arithmetic quotients of bounded symmetric domains. She also intends to work on questions about the fields obtained by adjoining torsion points on Abelian Varieties. 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.