Mathematical Sciences: Studies in Commutative Algebra and Its Applications to Computational Algebra

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This award supports the study of Cohen-Macaulay structures, in algebra, combinatorics, and geometry and is driven by their wide presence and the opportunities offered in issues of computational complexity. The principal investigator will investigate invariants of blowup algebras for their role in deciding the property of Cohen-Macaulay; will contribute to the ongoing process of algebraization of tangent and secant algebras; will study the role of various measures of complexity in the processing of basic operations of computational algebra; and will develop methods and algorithms that facilitate the efficient processing in large scale computations in cDaljit Ahlu geometry. This project is in the general area of computational algebra and the computer-aided computational aspects of this field. There is a growing interest in using computers to answer theoretical questions in algebra and conversely, algebra is quite useful for the development of algorithms. This research will not only aid in the development of computer programs in commutative algebra but will influence the development of computer programs in other areas. One aspect of this project concerns the development of a computer program which will solve systems of polynomial equations. This is significant in manufacturing both for modeling and for the development of robots.