Mathematical Sciences: A Software System for Algebraic Geometry Research

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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.