Mathematical Sciences: Tight Closures of Ideals, Linkage, and Hilbert Functions

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This project is concerned with three topics in commutative algebra. The principal investigator will study the theory of tight closures of ideals, the theory of algebraic linkage, and the behavior of the Hilbert function of m-primary ideals especially as it relates to the study of symbolic powers of prime ideals and the integral closures of ideals. This award supports the study of questions in commutative algebra and algebraic geometry. This is a rapidly developing area which impacts many areas of mathematics.