Mathematical Sciences: Homological Questions in Commutative Algebra

该奖项涉及某些研究 不变量，称为局部Chern字符，为模块定义 在当地的戒指。 这些不变量已被定义为有界的 自由模的复形 首席研究员将研究 由这些定义的各个矩阵的贡献 配合物 他还将考虑有关 多重性和其他理想理论性质。 结果 这些研究将被应用于同源结构， 相关问题。 这是代数几何领域的研究， 现代数学中最古老的部分，但其中有一个 在过去的四分之一个世纪里，革命性的开花。 在其 起源，它处理的数字，可以定义在平面上， 最简单的方程，即多项式。 目前，该领域 不仅使用代数方法，而且使用分析方法， 拓扑学，反过来说， 以及理论计算机科学和机器人技术。

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.