Mathematical Sciences: Problems in Algebraic Geometry

点击翻译按钮获取中文摘要

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.