Mathematical Sciences: Vector Bundles, Vanishing Theorems, and Syzygies

点击翻译按钮获取中文摘要

This award supports the research of Professor L. Ein to work in algebraic geometry. Professor Ein will study vector bundles and syzygies of algebraic varieties. He wishes to study the relationship between vector bundles, vanishing theorems and syzygies. This research is in the field of algebraic geometry, one of the oldest parts of modern mathematics. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields. Moreover, it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.