Mathematical Sciences: Research in Commutative Algebra and Invariant Theory

这个项目是关于交换 代数和不变式理论主要研究者 试图找到经典的幂零轨道方程 群并检验绿色猜想的一般正则 曲线.在二进制形式领域，他计划应用他的 技术来攻击Dixlane的猜想系统， 二进制形式的不变量环的参数。 本项目涉及的接口的研究 交换代数和代数几何。给定曲线， 交换代数可以与之相关联。信息 从研究交换代数用品 关于曲线的信息这是一个发展迅速的领域 影响了数学的许多领域。

This project is concerned with research in commutative algebra and invariant theory. The principal investigator intends to find the equations of nilpotent orbits for classical groups and examine Green's conjecture for general canonical curves. In the area of binary forms, he plans to apply his techniques to attack Dixmier's conjecture on systems of parameters for rings of invariants of binary forms. 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.