Mathematical Sciences: Motives and Algebraic Cycles

该奖项支持动机和代数循环方面的工作。 其中一个主要调查员会调查动机 上同调; Riemann-Roch的非阿基米德推广 Gillet和Soule证明的类型定理;以及 岩泽理论的周期和动机。 其他主要 调查人员将研究是否存在更高的 使用某些线性构型的族， 格拉斯曼主义者，以及探索 Grassmannian复形与基场的K-群 这是代数几何领域的研究， 现代数学中最古老的部分，但其中有一个 在过去的四分之一个世纪里，革命性的开花。 在其 起源，它处理的数字，可以定义在平面上， 最简单的方程，即多项式。 目前，该领域 不仅使用代数方法，而且使用分析方法， 拓扑学，反过来说， 以及理论计算机科学和机器人技术。

This award supports work on motives and algebraic cycles. One of the principal investigators will work on motivic cohomology; a non-archimedean generalization of the Riemann-Roch type theorem proved by Gillet and Soule; and a generalization of Iwasawa theory to cycles and motives. The other principal investigator will work on the existence of higher logarithms using families of certain linear configurations over the Grassmannians, as well as explore the relationship between the Grassmannian complex and the K-groups of the ground field. This is research in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origins, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays, the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in theoretical computer science and robotics.