Mathematical Sciences: Vector Bundles and Projective Geometry

该奖项支持伊利诺伊大学芝加哥分校劳伦斯·伊恩教授在代数几何方面的研究。Ein博士有几个项目，都与向量丛和射影几何之间的关系有关。在这些项目中，有研究特殊的Cremona变换、对偶簇和一般正则曲线的合子。这是对代数几何领域的研究，它是现代数学中最古老的部分之一，但在过去的25年里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，这个领域不仅使用了代数的方法，而且使用了分析和拓扑学的方法，相反，它在这些领域以及理论计算机科学和机器人学中都得到了应用。

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.