Mathematical Sciences: Semi-simple Groups and Arithmetic Subgroups

普拉萨德教授将致力于算术，几何和 上半单群的群论问题 局部和全局字段。 他打算研究 整体上各向异性半单群子群问题 功能字段。他还打算研究主丛， 某些光滑的品种。 这个项目福尔斯属于算术的一般范畴 几何学-一个融合了两个最古老的领域的主题， 数学：数论和几何。 这种组合有 被证明是非常富有成效的-最近解决了一些问题 经受住了几代人的考验 在其众多后果中， 纠错码 这些准则对现代和 计算机（硬盘）和光盘。

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.