Mathematical Sciences: Semi-simple Groups and Arithmetic Subgroups

Prasad教授将研究与局部和全局半单群相关的算术、几何和群论问题。他打算研究全局函数域上各向异性半简单群的同余子群问题。他还打算研究某些光滑品种的主束。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 Prasad will work on arithmetic, geometric and group theoretic questions related to semi-simple groups over local and global fields. He intends to work on the congruence subgroup problem for anisotropic semi-simple groups over global function fields. He also intends to study principal bundles over certain smooth 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.