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

9314761瓦斯康塞洛斯这个美国-墨西哥奖项将支持罗格斯大学的沃尔默·瓦斯康塞洛斯教授与墨西哥城国家理工学院的拉斐尔·比利亚雷亚尔教授合作。研究人员打算研究交换代数的理论方面，以及与组合学和计算代数的应用联系。更具体地说，该项目将集中研究与组合兴趣理想相关的分次环、Gorenstein代数、某些环簇的Cohen-Macaulay性以及它们在Grobner基理论中可能扮演的角色。这两位研究者都对交换代数中的中心问题感兴趣，特别是在大量不确定项中寻找多项式方程组的解并检测其中的Cohen-Macaulay结构的目的。研究人员打算通过电子邮件和电话联系、出席会议和定期访问计划来开展这项研究，该计划将有其他国家的研究生和他们的合作者参与。***

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. ***