Mathematical Sciences: Research in Commutative Algebra

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This project is concerned with research in commutative algebra related to geometric invariant theory. The principal investigator plans to find the equations of nilpotent orbits for classical groups. In the area of binary forms, he plans to further investigate the stratification by root multiplicities. In the area of hyperdiscriminants, he plans to describe the Whitney stratifications induced by them. 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.