Mathematical Sciences: Research in Algebraic Geometry and Related Topics

数学科学：代数几何及相关主题的研究

• 批准号: 9400550
• 负责人: Valery Lunts
• 金额: $ 4.94万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400550&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Algebraic; Geometry

Professor Youssin will investigate singularities of complex algebraic varieties. He will study the relationship between decompositions of the L-2 cohomology that come from intersection cohomology and those that come from modules over rings of differential operators. He also intends to study relations between Newton polyhedra and resolution of singularities. This is research in the field of algebraic geometry. Algebraic geometry is 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 physics, theoretical computer science, and robotics.

尤辛教授将研究复代数簇的奇点。他将研究来自交上同调的L-2上同调的分解与来自微分算子环上的模的上同调的分解之间的关系。他还打算研究牛顿多面体和奇点分解之间的关系。这是在代数几何领域的研究。代数几何是现代数学中最古老的部分之一，但在过去的25年里，它已经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，反过来，在这些领域以及物理、理论计算机科学和机器人中也找到了应用。