Some Problems in Equivariant Geometry & Representation Theory

等变几何中的一些问题

• 批准号: 9401018
• 负责人: Valery Lunts
• 金额: $ 6万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401018&HistoricalAwards=false
• 关键词: Some; Problems; Equivariant; Geometry; &amp

9401018 Lunts Professor Lunts will work on problems in the foundations of representation theory and algebraic geometry. In particular he will continue his study of the equivariant derived category of sheaves with a view to applications in equivariant geometry and representation theory. This is research in the field of algebraic geometry. Algebraic geometry itself 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.

小行星9401018 教授伦茨将工作的问题在基础上的代表性理论和代数几何。特别是，他将继续他的研究等变派生类别的层，以期应用在等变几何和代表性理论。 这是代数几何领域的研究。 代数几何本身是现代数学中最古老的部分之一，但在过去的四分之一世纪里，它已经有了革命性的发展。在其起源，它处理的数字，可以定义在平面上的最简单的方程，即多项式。如今，该领域不仅使用代数方法，还使用分析和拓扑学方法，相反，这些方法在这些领域以及物理学，理论计算机科学和机器人学中也得到了应用。