Mathematical Sciences: Anti Self-dual Connections on Algebraic Surfaces

数学科学：代数曲面上的反自对偶联系

• 批准号: 8904922
• 负责人: David Gieseker
• 金额: $ 9.21万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8904922&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Anti; Self; dual

This award supports the research in Algebraic Geometry of Professor David Gieseker of the University of California at Los Angeles. Dr. Gieseker's investigations will be in the isospectral theory of difference operators, considering the Picard group of the Bloch manifold of a two-dimensional periodic difference operator. He will also explore generalizations of the Bloch manifold construction to other contexts such as the triangular- ization of a surface of arbitrary genus. This is research in the field of Algebraic Geometry, 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 theoretical Computer Science, Robotics, and Physics.

该奖项支持加州大学洛杉矶分校的David Gieseker教授在《代数几何》中的研究。Gieseker博士的研究将在差分算子的等谱理论中进行，考虑二维周期差分算子的Bloch流形的Picard群。他还将探索Bloch流形结构对其他上下文的推广，例如任意亏格曲面的三角化。这是对代数几何领域的研究，它是现代数学中最古老的部分之一，但在过去的25年里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，相反，在这些领域以及理论计算机科学、机器人学和物理学中都有应用。