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: 0604885
• 负责人: Kevin Wortman
• 金额: $ 10.87万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2007-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604885&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.

该项目旨在将群体动作的特性与均匀空间，欧几里得建筑物和模量空间联系起来。调查的特殊性问题包括：（1）半神经谎言基团的离散群的准静态。 （2）有限属性偏离磁场算法（带有kai-uwe bux）。 （3）dehn功能的Arithmetic组（与Gregory Margulis）。 （4）在Abelian差异的空间上（带有Kariane calta）的单位流动。均匀空间是几何对象，可用于分析满足某些方程的数字数组。欧几里得建筑物也是几何对象，它们可用于研究广义种类的``数字''阵列。模量空间是几何对象，可用于将与复数方程相关的空格参数化。在比较和对比这三个对象方面已经付出了很多努力，因为每个对象在数学领域都起着重要作用。该项目的目的是继续研究这三个基本对象之间的联系，希望对三个之间的关系有更深入的了解，将对每个人作为个人有见识。