Mathematical Sciences: Algebraic Geometry and Gauge Theory

该奖项支持R.弗里德曼 来研究代数几何。 他将继续研究 的代数性质和光滑性质之间的联系 四维流形 特别是，他将试图决定，如果每一个 复曲面与有理曲面同构， 合理的，以及是否可以顺利地嵌入 2-位于复杂表面上的某些类型的球体。 这项研究是在代数几何领域，其中一个 现代数学中最古老的部分，但其中一个 在过去的10年里， 已经屹立了几个世纪最初，它把数字 在平面上由最简单的方程定义，即 多项式 今天，该领域使用的方法不仅来自 代数，但也从分析和拓扑学，反过来说，它 广泛应用于这些领域。 此外，它还证明， 它本身在物理学、理论、 计算机科学、密码学、编码理论和机器人技术。

This awards supports the research of Professor R. Friedman to work in algebraic geometry. He will continue to study the connections between the algebraic and smooth properties of 4-manifolds. In particular, he will try to decide if every complex surface diffeomorphic to a rational surface is itself rational and whether one can characterize smoothly embedded 2-spheres of certain types lying on a complex surface. The research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past 10 years, solved problems that have stood for centuries. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields. Moreover, it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.