Some Questions in Commutative Algebra

拟议的项目是在交换代数领域，这是一个研究系统的代数（多项式）方程的解决方案，在交换环。一个交换环可以被看作是一个抽象的模拟的整数，其中一个可以加，减和乘。在过去的几十年里，交换代数不仅与数学中的其他研究领域有着显著的相互作用，而且被证明是其他学科（如工程和计算机科学）的宝贵工具。 PI将涉及研究生在他的研究。PI将在交换代数中出现的几个项目的工作。他将调查当地的上同调模块（例如消失和有限性）和它们的连接与拓扑的代数簇和研究奇异性的特征p和他们的不变量。

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.