Mathematical Sciences: Fundamental Groups of Complex Manifolds

该奖项支持J. Carlson教授的研究 和D.托莱多在代数几何工作。 他们将 复流形的基本群及其 表示。 他们打算研究表征理论 最近构造的流形的例子， 非剩余有限基本群 他们还打算 应用调和映射理论扩大群的类 沙法雷维奇猜想是正确的 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 Professors J. Carlson and D. Toledo to work in algebraic geometry. They will work on fundamental groups of complex manifolds and their representations. They intend to study the representation theory of the recently constructed examples of manifolds with non-residually finite fundamental groups. They also intend to apply the theory of harmonic maps to enlarge the class of groups for which the Shafarevic conjecture is known to be true. 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.