Mathematical Sciences: Polylogarithms, Mixed Motives, and Special Values of L-Functions

Goncharov 9400010 教授贡恰罗夫将工作的古典和现代理论之间的关系的多对数和特殊价值的L-函数的品种。他还将探索代数k理论和motivic伽罗瓦群之间的联系。 我们的目标是一个明确的计算贝林森调节器的算术品种。 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。

Goncharov 9400010 Professor Goncharov will work on the relationship between both classical and modern theories of the polylogarithm and special values of L-functions of varieties. He will also explore connections between algebraic k-theory and motivic Galois groups. The goal is an explicit computation of the Beilinson regulator for arithmetic 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.