Mathematical Sciences: A Software System for Algebraic Geometry Research

该奖项支持M.Stillman教授继续开发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。他还希望研究射影簇的合子与簇的几何之间的关系。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。这里正在开发的软件将使这一领域中许多以前难以或不可能进行的计算成为可能。

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.