Mathematical Sciences: Commutative Rings and Differential Graded Algebras

这个项目涉及交换环和微分分次代数的同调理论中的几个主题。这项研究的一个主题是，将环的经典同调理论中的许多问题放在更广泛的微分分次代数的背景下，可以最有效地处理这些问题。主要研究者还将研究有限平坦维度的同态。本文研究的是代数几何与交换代数的接口问题。这是目前一个非常活跃的领域，其中相关的交换代数被用来获得关于潜在几何对象的精细知识。

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.