Mathematical Sciences: Topics in Arithmetic Geometry and K-theory

Gillet教授将继续他在Arekelov理论和代数K-理论方面的工作。他希望研究非阿基米德的阿雷凯洛夫理论。他还打算研究K-理论与动机之间的联系，特别是利用动机来构建一个具有紧凑支撑的K-理论。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。

Professor Gillet will continue his work on Arekelov theory and algebraic K-theory. He wishes to study non-archimedean Arekelov theory. He also intends to study the connections between K-theory and motives in particular to use motives to construct a K-theory with compact support. 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.