Mathematical Sciences: Homological Questions in Commutative Algebra

这个项目涉及交换代数中的几个猜想。首席研究员将考虑单项猜想和改进的新交集猜想。建议通过推广以往成功的方法以及使用一些新的同调方法来研究这些问题。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 conjectures in commutative algebra. The principal investigator will consider the monomial conjecture and the improved new intersection conjecture. It is proposed to study these questions by attempting to extend the methods which have been successful in the past as well as using some new homological methods. 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.