Mathematical Sciences: Structure of Algebraic Varieties

该奖项支持犹他大学的Janos Kollar教授在代数几何方面的研究。Kollar博士计划在快速发展的三倍和比三倍更高维度的代数变量最小模型领域工作。他还将利用Mori关于最小模型的新结果，在代数曲面理论和曲面奇点变形理论中寻找新的应用。这是代数几何领域的研究，代数几何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，还使用分析和拓扑的方法，并且反过来在这些领域以及理论计算机科学和机器人技术中得到应用。

This award supports the research in Algebraic Geometry of Professor Janos Kollar of the University of Utah. Dr Kollar plans to work in the rapidly developing field of minimal models for threefolds and algebraic varieties of higher dimension than three. He will also use the new results of Mori on minimal models to look for new applications in the theory of algebraic surfaces and the deformation theory of surface singularities. 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.