Mathematical Sciences: Overconstrained Mechanisms and Complex Algebraic Geometry

该奖项支持A.Sommese教授致力于将代数几何应用于数值分析和连杆问题的研究。特别是过度约束机制理论产生的问题。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，但它也应用于工程的许多领域。本提案所支持的研究表明了这一曾经纯粹的理论领域对机器人和制造的重要性。

This award supports the research of Professor A. Sommese to work on the applications of algebraic geometry to numerical analysis and problems in linkages. In particular problems arising from the theory of over-constrained mechanisms. 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, but it has applications to many areas of engineering as well. The research supported in the present proposal shows the importance of this once purely theoretical area for robotics and manufacturing.