Some Questions in Commutative Algebra

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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.