Mathematical Sciences: Finite Local Cohomology Rings and Minimally Regular Local Rings

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The research involved is in two distinct but related areas of local commutative algebra. One area is the study of systems of parameters in local rings whose smaller local cohomology modules have finite length and the effect of blowing-up an ideal generated by a system of parameters on such. The second area is the study of minimal birational regular local rings and connections with the regular closure of ideals. This project involves research on the interface of commutative algebra and algebraic geometry. Given a curve, a commutative algebra can be associated with it. Information derived from studying the commutative algebra supplies information about the curve. This is a rapidly developing area which impacts many areas of mathematics.