Mathematical Sciences: Topics in Arithmetic Geometry and K-theory

吉莱教授将继续他对阿拉克洛夫理论的研究 和算术Riemann-Roch型定理。 他还将致力于 代数K-理论中的Gersten猜想与联系 Lichtenbaum关于K理论和调节器的论述之间， 算术交理论 这个项目福尔斯属于算术的一般范畴 几何--一门融合了几何学两个最古老领域的学科 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 Gillet will continue his work on Arakelov theory and arithmetic Riemann-Roch type theorems. He will also work on Gersten's conjecture in Algebraic K-theory and connections between Lichtenbaum's conjectures on K-theory and Regulators and arithmetic intersection theory. 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.