Mathematical Sciences: Space Curves Which Are the Intersection of Two Surfaces

该奖项支持D. Jaffe教授在代数几何方面的研究工作。他将研究复杂投影三维空间中的曲线和曲面。特别地，他将研究这样一个猜想：一个平滑连接的曲线，如果它的度超过它的格至少四倍，它就不是两个曲面的交点。这项研究属于代数几何领域，是现代数学中最古老的部分之一，但在过去10年里，它发展到解决了几个世纪以来一直存在的问题的程度。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 D. Jaffe to work in algebraic geometry. He will work on curves and surfaces in complex projective three-space. In particular, he will work on the conjecture that a smooth connected curve, whose degree exceeds its genus by at least four, is not an intersection of two surfaces. This 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.