Mathematical Sciences: Topics in Arithmetic Geometry and K-theory

Gillet教授将继续他在Arakelov理论和算术Riemann-Roch型定理方面的工作。他还将研究Gersten在代数k理论中的猜想以及Lichtenbaum在k理论和调节器以及算术交集理论中的猜想之间的联系。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 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.