Mathematical Sciences: Topology and Algebraic Geometry

数学科学：拓扑和代数几何

• 批准号: 9218215
• 负责人: Aaron Bertram
• 金额: $ 4.87万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-09-01 至 1995-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9218215&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topology; Algebraic; Geometry

This awards supports the research of Professor A. Bertram to work in algebraic geometry. He will study the moduli spaces of vector bundles on an algebraic curve. In particular he hopes to derive a rigorous proof of the empirically observed formula of Verlinde and Witten for studying the cohomology groups associated to these moduli spaces. 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.

该奖项支持A. Bertram教授在代数几何学上工作的研究。 他将在代数曲线上研究向量束的模量空间。特别是他希望得出严格的证据证明Verlinde和Witten的经验观察到的公式，以研究与这些模量空间相关的同胞组。 这项研究是在代数几何的领域，这是现代数学的最古老部分之一，但它蓬勃发展到过去10年中，它解决了已经存在了几个世纪的问题。最初，它处理了在平面中通过最简单的方程式（即多项式）定义的数字。如今，该领域不仅使用代数的方法，而且使用分析和拓扑的方法，相反，它在这些领域中广泛使用。 此外，它已经证明了自己在物理，理论计算机科学，密码学，编码理论和机器人技术等多样化的领域中有用。