Group actions on homogeneous spaces, Euclidean buildings, and moduli spaces

齐次空间、欧几里得建筑和模空间的群作用

• 批准号: 0750032
• 负责人: Kevin Wortman
• 金额: $ 7.39万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-05-18 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0750032&HistoricalAwards=false
• 关键词: Group; actions; homogeneous; spaces; Euclidean

This project is aimed at relating properties of group actions onhomogeneous spaces, Euclidean buildings, and moduli spaces. Specifictopics for investigation include: (1) Quasi-isometries of discretesubgroups of semisimple Lie groups. (2) Finiteness properties offunction-field-arithmetic groups (with Kai-Uwe Bux). (3) Dehn functions ofarithmetic groups (with Gregory Margulis). (4) Unipotent flows on spacesof abelian differentials (with Kariane Calta).Homogeneous spaces are geometric objects that can be used to analyze arrays of numbers that satisfy certain equations. Euclidean buildings are also geometric objects, and they can be used to study arrays of generalized kinds of ``numbers''. Moduli spaces are geometric objects that can be used to parameterize spaces related to equations of complex numbers. Much effort has been put into comparing and contrasting these three objects, as each plays a significant role in the field of mathematics. The goal of this project is to continue to examine links between these three fundamental objects with the hope that a deeper understanding of the relationships between the three will bear insights for each as individuals.

该项目旨在将同质空间、欧几里得建筑和模空间上的群体行为的属性联系起来。研究的具体主题包括：（1）半单李群的离散子群的拟等距。 (2) 函数域算术群的有限性性质（与 Kai-Uwe Bux）。 (3) 算术群的 Dehn 函数（与 Gregory Margulis 合作）。 (4) 阿贝尔微分空间上的单能流（与 Kariane Calta 合作）。齐次空间是可用于分析满足某些方程的数字数组的几何对象。欧几里得建筑也是几何对象，它们可用于研究广义类型“数字”的数组。模空间是可用于参数化与复数方程相关的空间的几何对象。人们投入了大量精力来比较和对比这三个对象，因为它们在数学领域中都发挥着重要作用。该项目的目标是继续研究这三个基本对象之间的联系，希望更深入地了解这三个对象之间的关系将为每个个体带来见解。