Mathematical Sciences: Vector Bundles, Vanishing Theorems, and Syzygies

该奖项支持L. Ein教授在代数几何方面的研究工作。Ein教授将研究向量束和代数变种的合成性。他希望研究向量束之间的关系，消失定理和协同。这项研究是在代数几何领域，这是现代数学最古老的部分之一。最初，它用最简单的方程，即多项式来处理平面上定义的图形。今天，该领域不仅使用代数的方法，而且还使用分析和拓扑的方法，相反，它在这些领域中被广泛使用。此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人等多种领域都很有用。

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.