Mathematical Sciences: Commutative Rings and Differential Graded Algebras

本课题涉及交换环和微分梯度代数的同调理论中的几个主题。本研究的一个主题是，在环的经典同调理论中出现的许多问题，通过将它们置于更广泛的微分梯度代数的背景下，可以最有效地处理。首席研究员还将研究有限平面维的同态。本研究是代数几何与交换代数的交叉领域。这是目前一个非常活跃的领域，其中使用关联交换代数来获得有关底层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.