Mathematical Sciences: Overconstrained Mechanisms and Complex Algebraic Geometry

点击翻译按钮获取中文摘要

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.