Mathematical Sciences: Moduli of Vector Bundles and other Problems in Algebraic Geometry

该奖项支持宾夕法尼亚大学罗恩·多纳吉教授在代数几何方面的研究。多纳吉博士的项目主要涉及曲线上向量丛的模数，但他也将花费时间研究代数完全可积系统和肖特基问题。代数几何是现代数学中最古老的部分之一，但在过去的25年里，它已经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，该领域不仅使用代数的方法，而且使用分析和拓扑学的方法，反过来，在这些领域以及物理、理论计算机科学和机器人中也找到了应用。

This award supports the research in algebraic geometry of Professor Ron Donagi of the University of Pennsylvania. Dr. Donagi's project is concerned mostly with the moduli of vector bundles on a curve, but he will also spend time investigating algebraically completely integrable systems and the Schottky problem. Algebraic geometry is 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 physics, theoretical computer science, and robotics.