Mathematical Sciences: Algebraic Transformation Groups & Invariant Theory

这个项目是关于代数群的研究。主要研究人员将研究还原复代数群在复n-空间上的作用，以努力将那些不能线性化的作用分类。他还将研究一个猜想，即复仿射簇的商空间上的微分算子代数是有限生成的。所支持的研究涉及不变理论和代数群。一般而言，不变量理论涉及线性代数群在流形或线性空间上的作用，以及在这些群作用下空间的数学不变量的确定。

This project is concerned with research on algebraic groups. The principal investigator will study the action of a reductive complex algebraic group on complex n-space in an effort to classify those actions which cannot be linearized. He will also investigate the conjecture that the algebra of differential operators on quotient spaces of a complex affine variety is finitely generated. The research supported involves invariant theory and algebraic groups. In general, invariant theory involves the actions of linear algebraic groups on manifolds or linear spaces and the determination of the mathematical invariants of the space under these group actions.