Mathematical Sciences: Topics in Arithmetic Geometry and K-theory

吉莱教授将继续他的工作Arekelov理论和代数K理论。他希望研究非阿基米德的阿雷克洛夫理论。他还打算研究K-理论和动机之间的联系，特别是利用动机来构建一个具有紧支撑的K-理论。 这个项目福尔斯属于算术几何的一般领域-一个融合了两个最古老的数学领域：数论和几何的主题。 事实证明，这种结合非常富有成效--最近解决了几代人都无法解决的问题。 在它的许多后果是新的纠错码。 此类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.