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教授的研究。伯特伦到 研究代数几何。 他将研究的模空间 代数曲线上的向量丛他特别希望， 推导出经验观察公式的严格证明 Verlinde和维滕研究了相关的上同调群 到这些模空间。 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，该领域不仅使用代数方法， 也来自于分析和拓扑学，相反， 广泛应用于这些领域。 此外，它还证明了自己 在物理学、理论计算机、 科学、密码学、编码理论和机器人技术。