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

这个项目涉及交换中的三个主题 代数首席研究员将研究 紧封闭的理想，理论的代数联系，和 m-准素理想的Hilbert函数的性态 特别是当它涉及到素数的符号幂的研究时， 理想和理想的积分闭包。 该奖项支持交换问题的研究 代数和代数几何。这是一个发展迅速的领域 影响了数学的许多领域。

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.