Mathematical Sciences: Topics in Algebra and Geometry

该奖项支持芝加哥伊利诺伊大学Henri Gillet教授在k理论和代数几何方面的研究。在继续与C. Soule的合作中，他计划研究算术变量的代数不变量和微分几何不变量之间的关系，并可能将这些结果应用于数论问题。Gillet博士的另一个项目是继续与Peter Shalen博士共同研究广义树上群的作用，并利用这些作用来获得有关群的上同调的信息。这是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，但在过去的四分之一个世纪里，它已经有了革命性的发展。在它的起源中，它处理的图形可以用最简单的方程，即多项式，在平面上定义。如今，该领域不仅使用代数的方法，还使用分析和拓扑的方法，并且反过来在这些领域以及理论计算机科学和机器人技术中得到应用。

This award supports the research in K-Theory and Algebraic Geometry of Professor Henri Gillet of the University of Illinois at Chicago. In continuing joint work with C. Soule, he plans to investigate the relationship between algebraic and differential- geometric invariants of arithmetic varieties, and possibly to apply these results to questions in number theory. Another project of Dr. Gillet is to continue joint work with Dr. Peter Shalen in studying the actions of groups on generalized trees, with the idea of using these actions to obtain information about the cohomology of the groups involved. 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 origin, 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 in Robotics.