Mathematical Sciences: Vector Bundles and Projective Geometry

该奖项支持伊利诺伊大学芝加哥分校Lawrence Ein教授在代数几何方面的研究。艾因博士有几个项目，都与矢量束和射影几何之间的关系有关。这些项目包括研究一般正则曲线的特殊克雷莫纳变换、对偶变异和共合。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 Algebraic Geometry of Professor Lawrence Ein of the University of Illinois at Chicago. Dr. Ein has several projects, all concerned with the relation between vector bundles and projective geometry. Among these projects are the study of special Cremona transformations, dual varieties and syzygies of the generic canonical curve. 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.