Mathematical Sciences: Harmonic Mappings, Discrete Groups, and Hodge Theory

该奖项支持犹他大学的詹姆斯·卡尔森教授和多明戈·托莱多教授在代数几何方面的研究。他们的工作是在Hodge理论中进行的，他们的目的是解决从紧Kaehler流形到非紧型局部对称空间的调和映射的分类问题，特别注意刚性和因式分解定理。这是对代数几何领域的研究，它是现代数学中最古老的部分之一，但在过去的25年里取得了革命性的成就。在它的起源中，它处理的是可以在平面上用最简单的方程定义的图形，即多项式。如今，这个领域不仅使用了代数的方法，而且使用了分析和拓扑学的方法，相反，它在这些领域以及理论计算机科学和机器人学中都得到了应用。

This award supports the research in Algebraic Geometry of Professors James Carlson and Domingo Toledo of the University of Utah. Their work is in Hodge theory, and their aim is to attack the problem of classifying harmonic mappings from compact Kaehler manifolds to locally symmetric spaces of noncompact type, with particular attention to rigidity and factorization theorems. 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.