Mathematical Sciences: A Software System for Algebraic Geometry Research

该奖项支持M. Stillman教授的研究，继续发展Macaulay 2。该系统将使处理多变量多项式方程组的大规模研究计算项目成为可能。他还希望研究射影品种的共合性与品种几何的关系。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。这里正在开发的软件将使这个领域许多以前困难或不可能的计算成为可能。

This awards supports the research of Professor M. Stillman to continue the development of Macaulay 2. This system will enable large scale research computing projects dealing with systems of polynomial equations in many variables. He also hopes to work on the relationship of syzygies of a projective variety to the geometry of the variety. 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. The software being developed here will make many previously difficult or impossible computations in this field possible.