Mathematical Sciences: Studies in Commutative Algebra and Algebraic Geometry

该奖项支持交换代数的研究， 梅尔文·霍希斯特、伊戈尔·多尔加切夫、 以及密歇根大学安阿伯分校的凯文·库姆斯。博士 Hochster介绍了紧密封闭的富有成效的概念， 戒指，并将继续他对这一概念的研究，以及 局部代数中的几个问题多尔加乔夫医生将在 关于Enriques曲面的分类 自同构域的任意特征，并将 研究理论中的一些其他问题 表面。库姆斯博士会学习更多的数论 问题，即算术曲面的几何，特别是 算术曲面的分支覆盖理论 在算术兴趣域上定义的曲线。 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。如今，该领域 使用的方法不仅从代数，但从分析和 拓扑学，反过来说， 以及理论计算机科学和机器人学。

This award supports the research in commutative algebra and algebraic geometry of Professors Melvin Hochster, Igor Dolgachev, and Kevin Coombes of the University of Michigan at Ann Arbor. Dr. Hochster has introduced the fruitful notion of tight closure of rings, and will continue his study of this concept, as well as several problems in local algebra. Dr. Dolgachev will be working on the classification of Enriques surfaces with finitely many automorphisms over fields of arbitrary characteristic, and will investigate a number of other questions in the theory of surfaces. Dr. Coombes will be studying more number-theoretic questions, namely the geometry of arithmetic surfaces, especially the theory of branched covers of arithmetic surfaces and of curves defined over fields of arithmetic interest. 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 origin, 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 in Robotics.