Mathematical Sciences: Computer Assisted Studies in Commutative Algebra

本项目旨在研究Cohen-Macaulay环和代数，并有效地计算它们的不变量。它的目的是揭示和推广Koszul同调在Cohen-Macaulay奇点结构理论中的作用，研究线性类型代数的结构，检验符号幂代数的方程，研究交换李代数的不变量和奇点及其表示；并开发允许在交换代数中进行超大规模计算的方法和算法。这项研究是在交换代数的一般领域和该领域的计算机辅助计算方面进行的。人们对使用计算机回答理论问题的兴趣与日俱增。这个项目认真地利用符号计算的理论和实践来解决交换代数中的实际问题。

This project is directed at studying Cohen-Macaulay rings and algebras, and effectively computing their invariants. Its aims are to uncover and extend the role of Koszul homology in the structure theory of Cohen-Macaulay singularities; to investigate the structure of the algebras of linear type; to examine the equations of symbolic power algebras; to study the invariants and singularities of commuting varieties of Lie algebras and their representations; and to develop methods and algorithms that allow for very large scale computations in commutative algebra. This research is in the general area of commutative algebra and the computer-aided computational aspects of this field. There is a growing interest in using computers to answer theoretical questions. This project makes serious use of both the theory and practice of symbolic calculations to solve real problems in commutative algebra.