Mathematical Sciences: Problems in Algebraic Geometry

该奖项支持在代数几何的研究， 加州大学的罗伯特·拉扎斯菲尔德教授在 洛杉矶。拉扎斯菲尔德博士将继续他的工作， 向量丛技术在线性问题研究中的应用 系列.他特别打算调查一些问题 涉及诺特-莱夫谢茨轨迹以及一些问题 加州大学洛杉矶分校的马克绿色博士已经开始了这项工作， 一般消失定理 这是代数几何领域的研究， 现代数学中最古老的部分，但其中有一个 在过去的四分之一个世纪里，革命性的开花。在其 起源，它处理的数字，可以定义在平面上， 最简单的方程，即多项式。如今，该领域 使用的方法不仅从代数，但从分析和 拓扑学，反过来说， 以及理论计算机科学和机器人学。

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.