Mathematical Sciences: Homological Questions in Commutative Algebra

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This project is concerned with several conjectures in commutative algebra. The principal investigator will consider the monomial conjecture and the improved new intersection conjecture. It is proposed to study these questions by attempting to extend the methods which have been successful in the past as well as using some new homological methods. This research is on the interface of algebraic geometry and commutative algebra. This is currently a very active area in which an associated commutative algebra is used to obtain refined knowlege about the underlying geometric object.