Mathematical Sciences: Research in Commutative Algebra and Invariant Theory

本研究将集中在三个方面： 代数、表示论和不变量理论。 在 交换代数，该项目将构建和研究 长度为3的分辨率的通用环。 代表性 理论，Littlewood-Richardson规则将被推广为 所有的经典群和旋量群 在不变量领域 理论上，首席研究员计划找到发电机， 并证明了M.绿色 亏格G的一般标准曲线猜想 交换代数的主要来源之一是19世纪 世纪不变量理论。 有限生成问题 形式环及其著名的解决方案希尔伯特是 交换代数和表示论的起点。 这个项目将调查这三者之间的联系 地区 可以预见，代数， 几何和表示论方法将导致 在这些领域取得重大进展。

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.