Some Questions in Commutative Algebra

提议的项目是在交换代数领域，这是一个代数（多项式）方程组的解在交换环的研究。交换环可以看作是整数的抽象类比，其中可以加、减、乘。在过去的几十年里，交换代数不仅在数学的其他研究领域发现了显著的相互作用，而且被证明是其他学科的有价值的工具，如工程和计算机科学。该项目将包括研究生参与他的研究。PI将从事交换代数中出现的几个项目。他将研究局部上同模的性质（如消失性和有限性）及其与代数变量拓扑的联系，并研究特征p的奇点及其不变量。

The proposed projects are in the area of commutative algebra, which is a study of systems of algebraic (polynomial) equations with solutions in commutative rings. A commutative ring may be viewed as an abstract analogue of the integers, in which one can add, subtract and multiply. In the past few decades, commutative algebra has not only found remarkable interactions with other research areas in mathematics, but proven a valuable tool to other disciplines, such as engineering and computer science. The PI will involve graduate students in his research.The PI will work on several projects arising in commutative algebra. He will investigate properties of local cohomology modules (e.g. vanishing and finiteness) and their connections with topology of algebraic varieties and study singularities in characteristic p and their invariants.