Mathematical Sciences: Problems in Algebraic Geometry

该奖项支持加州大学洛杉矶分校罗伯特·拉扎斯菲尔德教授在代数几何方面的研究。Lazarsfeld博士将继续研究向量丛技术在线性级数研究中的应用。特别是，他打算研究与Noether-Lefschetz轨迹有关的一些问题，以及与加州大学洛杉矶分校的Mark Green博士在一般消失定理方面已经开始的工作中出现的一些问题。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 Robert Lazarsfeld of the University of California at Los Angeles. Dr. Lazarsfeld will be continuing his work on the applications of vector bundle techniques in the study of linear series. In particular, he intends to investigate some problems involving the Noether-Lefschetz locus as well as some questions arising out of work already begun with Dr. Mark Green of UCLA, on generic vanishing theorems. 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.