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

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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. ***