U.S.-Mexico: Studies in Commutative Algebra with Applications to Combinatorics and Computer Algebra

9314761 Vasconcelos美国-墨西哥奖将支持罗格斯大学的Wolmer Vasconcelos教授与墨西哥城国家理工学院的Rafael Villarreal教授合作。 研究人员打算从事交换代数的理论方面的工作，并将其应用于组合数学和计算代数。 更具体地说，该项目将侧重于研究与组合感兴趣的理想相关的分次环，Gorenstein代数，某些环面品种的Cohen-Macaulayness以及它们在Grobner基础理论中可能发挥的作用。 这两个调查人员感兴趣的中心问题交换代数，特别是目的的解决方案，并检测科恩-麦考利结构，系统的多项式方程在大量的不确定性。研究人员打算通过电子邮件和电话联系，通过参加会议和通过定期访问计划进行这项研究，该计划将涉及其他国家的研究生及其合作者。 ***

9314761 Vasconcelos This U.S.-Mexico award will support Professor Wolmer Vasconcelos of Rutgers University in collaboration with Professor Rafael Villarreal of the Instituto Politecnico Nacional in Mexico City. The researchers intend to work on theoretical aspects of commutative algebra and applied links to combinatorics and computational algebra. More specifically, the project will focus on studying graded rings associated to ideals of combinatorial interest, Gorenstein algebras, the Cohen-Macaulayness of certain toric varieties and the role they may play in the theory of Grobner bases. Both investigators are interested in central questions in commutative algebra, particularly the aim of finding the solution of, and detecting Cohen-Macaulay structure in, systems of polynomial equations in a large number of indeterminates. The investigators intend to carry out this research through e-mail and telephone contact, by attendance to meetings and through a program of regular visits that will involve graduate students and their collaborators in other countries. ***