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.

这个奖项支持伯特伦教授在代数几何方面的研究。他将研究代数曲线上向量束的模空间。他特别希望对Verlinde和Witten的经验观察公式进行严格的证明，以研究与这些模空间相关的上同调群。这项研究是在代数几何领域进行的，代数几何是现代数学中最古老的部分之一，但在过去的10年里，它已经发展到解决了几个世纪以来一直存在的问题的程度。最初，它用最简单的方程，即多项式来处理平面上定义的图形。今天，该领域不仅使用代数的方法，而且还使用分析和拓扑的方法，相反，它在这些领域中被广泛使用。此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人等多种领域都很有用。