Mathematical Sciences: Commutative Rings and Differential Graded Algebras

该项目涉及交换环同调论和微分分级代数中的几个主题。 这项研究的一个主题是，通过将经典环同调理论中出现的许多问题置于微分分级代数的更广泛背景下，可以最有效地解决它们。 首席研究员还将研究有限平面维度的同态。 本研究是代数几何和交换代数的接口。 目前这是一个非常活跃的领域，其中使用相关的交换代数来获取有关基础几何对象的精确知识。

This project is concerned with several topics in the homological theory of commutative rings and differential graded algebras. A theme of this research is that many problems arising within the classical homological theory of rings are most effectively treated by placing them in the broader context of differential graded algebras. The principal investigator will also study homomorphisms of finite flat dimension. This research is on the interface of algebraic geometry and commutative algebra. This is currently a very active area in which an associated commutative algebra is used to obtain refined knowlege about the underlying geometric object.