Mathematical Sciences: Commutative Algebra

研究了局部环上的交换代数及其奇异性。具体的主题包括两个变换，点，多重性，希尔伯特函数，和整体封闭的理想。这项研究是在交换代数的一般领域，因为它适用于代数几何。首席研究员将继续研究代数定义的几何物体中的奇点问题。这是目前数学界感兴趣的一个话题。

This research is concerned with commutative algebra on local rings and their singularities. Specific topics include birational transforms, spots, multiplicities, Hilbert functions, and integrally closed ideals. This research is in the general area of commutative algebra as it applies to algebraic geometry. The principal investigator will continue to study the question of singularities in algebraically defined geometric objects. This is a topic of current interest in the mathematical community.