Algebraic Geometry & Commutative Algebra

[401256]格林格林教授将研究几何中的射影变分和交换代数问题。这些问题包括Castelnuovo理论、代数曲线的合子问题和一般初始理想问题。这是代数几何领域的研究。代数几何是现代数学中最古老的部分之一，但在过去的25年里，它已经有了革命性的发展。在它的起源中，它处理的图形可以用最简单的方程，即多项式，在平面上定义。如今，该领域不仅使用代数的方法，还使用分析和拓扑的方法，相反，它在这些领域以及物理学、理论计算机科学和机器人技术中也得到了应用。

9401256 Green Professor Green will investigate problems in the geometry of projective varieties and commutative algebra. These include problems in Castelnuovo theory, syzygies of algebraic curves and generic initial ideals. This is research in the field of algebraic geometry. Algebraic geometry is 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 physics, theoretical computer science, and robotics.