Mathematical Sciences: Homological Questions in Commutative Algebra

这个奖项是关于某些不变量的研究，被称为局部陈氏字符，为局部环上的模定义。这些不变量被定义为自由模的有界复合体。首席研究员将研究由这些复合物定义的单个矩阵的贡献。他还将考虑有关多样性和其他理想理论性质的问题。这些研究的结果将应用于同调猜想和相关问题。这是代数几何领域的研究，是现代数学中最古老的部分之一，但在过去的四分之一个世纪里，它已经有了革命性的发展。在它的起源中，它处理的图形可以用最简单的方程，即多项式，在平面上定义。如今，该领域不仅使用代数的方法，而且还使用分析和拓扑的方法，相反，它在这些领域以及理论计算机科学和机器人技术中也得到了应用。

This award is concerned with the study of certain invariants, known as local Chern characters, defined for modules over local rings. These invariants have been defined for bounded complexes of free modules. The principal investigator will study the contributions of individual matrices defined by these complexes. He will also consider questions concerning multiplicities and other ideal-theoretic properties. The results of these studies will be applied to homological conjectures and to related problems. This is research in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origins, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays, the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in theoretical computer science and robotics.