Mathematical Sciences: Hodge Theory and Algebraic Geometry

该奖项支持M.格林教授致力于代数几何的研究。他将致力于霍奇理论、射影簇几何和代数曲线的研究。所使用的技术将是代数和微分几何的混合体。这项研究是在代数几何领域进行的，代数几何是现代数学中最古老的部分之一，但在过去的10年里，它发展到了解决了几个世纪以来的问题的地步。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，这个领域不仅使用代数的方法，而且还使用分析和拓扑学的方法，相反，它在这些领域被广泛使用。此外，它在物理、理论计算机科学、密码学、编码理论和机器人学等领域都证明了自己的有用。

This awards supports the research of Professor M. Green to work in algebraic geometry. He will work on Hodge theory, the geometry of projective varieties, and algebraic curves. The techniques used will be a mixture of algebraic and differential- geometric. The research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past 10 years, solved problems that have stood for centuries. 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.