Mathematical Sciences: Commutative Rings and Differential Graded Algebras

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This project is concerned with several topics in the homological theory of commutative rings and differential graded algebras. A theme of this research is that many problems arising within the classical homological theory of rings are most effectively treated by placing them in the broader context of differential graded algebras. The principal investigator will also study homomorphisms of finite flat dimension. 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.