Mathematical Sciences: Algebraic Geometry

该奖项支持哥伦比亚大学教授亨利·平克姆、罗伯特·弗里德曼和大卫·拜尔在代数几何方面的研究。平卡姆博士和拜耳博士打算对现代数学中最具阻力的问题之一--雅克比猜想--进行计算和理论上的攻击。弗里德曼博士的项目涉及对代数曲面上稳定向量丛的模空间结构的持续研究。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 Professors Henry Pinkham, Robert Friedman, and David Bayer of Columbia University. Drs. Pinkham and Bayer intend to mount a computational and theoretical attack on one of the most resistant problems of modern mathematics, the Jacobian Conjecture. Dr. Friedman's project involves an ongoing investigation into the structure of moduli spaces of stable vector bundles on an algebraic surface. 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.