Mathematical Sciences: Research in Commutative Algebra and Invariant Theory

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This research will focus on three areas: commutative algebra, representation theory and invariant theory. In commutative algebra, the project will construct and study the generic ring for resolutions of length 3. In representation theory , the Littlewood-Richardson rule will be generalized for all classical and spinor groups. In the area of invariant theory, the principal investigator plans to find generators of multiplicity ideals for binary forms and prove the M. Green conjecture for general canonical curves of genus g. One of the main sources of commutative algebra was 19th century invariant theory. The problem of finite generation of rings of forms and its famous solution by Hilbert were the starting point of commutative algebra and representation theory. This project will investigate the connections between those three areas. It is anticipated that the combination of algebraic, geometric and representation theoretic methods will lead to substantial progress in those areas.