Mathematical Sciences: Studies in Algebraic Geometry

数学科学：代数几何研究

• 批准号: 9304732
• 负责人: Igor Dolgachev
• 金额: $ 7.2万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 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: 1993-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9304732&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Algebraic; Geometry

This awards supports the research of Professor I. Dolgachev to work in algebraic geometry. Professor Dolgachev will study relations between invariants and vector bundles. He also intends to study problems related to instantons and moduli spaces of vector bundles. This 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I教授的研究。多尔加切夫 来研究代数几何。 多尔加切夫教授将研究 不变量和向量丛之间的关系。他还打算 研究与向量的瞬子和模空间有关的问题 捆起来。 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， 已经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， 该领域不仅使用代数方法， 分析和拓扑学，相反，它被广泛用于 这些领域。 此外，它已证明自己在以下领域是有用的， 包括物理学、理论计算机科学、密码学、 编码理论和机器人学