Mathematical Sciences: Research in Commutative Algebra

本课题主要研究与几何不变量理论相关的交换代数。首席研究员计划找到经典群的幂零轨道方程。在二进制形式方面，他计划进一步研究根的多重性的分层。在过度歧视方面，他计划描述由它们引起的惠特尼分层。本项目涉及交换代数与代数几何的接口研究。给定一条曲线，一个交换代数可以与它联系在一起。从研究交换代数中得到的信息提供了有关曲线的信息。这是一个发展迅速的领域，对数学的许多领域产生了影响。

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.