Mathematical Sciences: On Several Homological Problems in Commutative Algebra

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This project is concerned with problems in commutative algebra and algebraic geometry. The principal investigator will work on the canonical element conjecture of Hochster and related problems. He will also consider the positivity part of Serre's conjecture on intersection multiplicity of modules. 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.