Mathematical Sciences: Stable Bundles on Algebraic Surfaces

数学科学：代数曲面上的稳定丛

• 批准号: 9305657
• 负责人: David Gieseker
• 金额: $ 6万
• 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: 1993
• 资助国家: 美国
• 起止时间: 1993-07-15 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9305657&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Stable; Bundles; Algebraic

This awards supports the research of Professor D. Gieseker to work in algebraic geometry. He will study stable bundles on algebraic surfaces and the theory of isospectral deformations of difference operators, in particular a two dimensional version of the Toda lattice will be studied. He will also investigate a possible method for computing Donaldson polynomials. 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D教授的研究。吉塞克， 研究代数几何。 他将研究稳定丛， 代数曲面和等谱形变理论 差分算子，特别是二维形式的 将研究户田晶格。 他还将调查 计算唐纳森多项式的可能方法。 这项研究是在代数几何领域，其中之一， 现代数学中最古老的部分，但其中一个蓬勃发展， 在过去的10年里，它解决了一些问题， 屹立了几个世纪 最初，它处理的是 平面由最简单的方程，即多项式。今天 field不仅使用代数方法，还使用分析方法 和拓扑学，相反，它被广泛用于那些 领域的 此外，它已经证明自己在各种领域都很有用， as physics物理，theoretical理论computer计算机science科学，cryptography密码学，coding编码 理论与机器人