Mathematical Sciences: Research in Algebra and Algebraic Number Theory

这项研究涉及到代数几何中的问题。主要的研究人员将继续他的动机上同调的研究，并建立与代数K-理论和DedekindZeta函数的值的联系。对Soule-Beilinson猜想和相关主题也有可能的应用，也将被探索。这是对代数几何领域的研究，代数几何是现代数学中最古老的部分之一，但在过去的25年里，它取得了革命性的成就。在它的起源中，它处理的是可以在平面上用最简单的方程定义的图形，即多项式。如今，这个领域不仅使用代数的方法，而且使用分析和拓扑学的方法，相反，在这些领域以及理论计算机科学和机器人学中找到了应用。

This research is concerned with problems in algebraic geometry. The principal investigator will continue his study of motivic cohomology and establishing connections with algebraic K-theory and the values of Dedekind zeta functions. There are possible applications to the Soule-Beilinson conjecture and related topics which will also be explored. 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.