Mathematical Sciences: Models for Hilbert Varieties and Galois Structure of deRham Cohomology

Pappas教授将研究算术几何特别是志村变量的坏约简理论侧重于Hilbert模变量的情况。他还将研究算术变异的DeRham上同调群的伽罗瓦结构。这个项目属于算术几何的一般领域，这个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 Pappas will work in arithmetic geometry specifically the theory of bad reduction of Shimura varieties concentrating on the case of Hilbert Modular varieties. He will also study the Galois structure of DeRham cohomology groups of arithmetic 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.