Cartan connections, geometry of homogeneous spaces, and dynamics

嘉当连接、齐次空间几何和动力学

• 批准号: 1057798
• 负责人: Karin Melnick
• 金额: $ 1.37万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-05-01 至 2013-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1057798&HistoricalAwards=false
• 关键词: Cartan; connections; geometry; homogeneous; spaces

"Workshop on Cartan Connections, Geometry of Homogeneous Spaces, and Dynamics" to be held at the Erwin Schroedinger Institute, July 11-22, 2011. The two-week workshop is devoted to two major themes, conformal geometry and its generalizations, and group actions on manifolds, and the discussion will be organized around techniques from Cartan geometries in these areas. Cartan geometries are a framework for study of a wide range of geometric structures, in which each such structure has an infinitesimal model that is a homogeneous space. The symmetry of this model leads to useful algebraic expressions for the geometric invariants of a given geometric manifold. A thorough understanding of existence and basic properties of Cartan geometries in most important contexts has recently been obtained, and the focus has shifted towards using the Cartan connection to study the geometries in question. Primary intellectual goals of the workshop are (1) to gather the diverse group of researchers currently working with Cartan geometries on a range of problems in geometry and analysis, and (2) introduce researchers working on the same problems to the techniques of Cartan geometries that have yielded valuable results.The themes of the workshop have important connections to physics, including general relativity and the AdS/CFT correspondence. The time period overlaps with a semester program on "Dynamics of General Relativity," and the organizers anticipate fruitful interaction among participants in the two events. A particular effort is being made to invite early-career researchers and mathematicians from underrepresented groups or working in developing countries.

“Cartan连接、均匀空间几何和动力学研讨会”将于2011年7月11日至22日在Erwin Schroedinger研究所举行。为期两周的研讨会致力于两个主要主题，保形几何及其推广，以及流形上的群作用，讨论将围绕这些领域的Cartan几何的技巧来组织。Cartan几何是研究范围广泛的几何结构的框架，其中每个这样的结构都有一个作为齐次空间的无穷小模型。这个模型的对称性导致了给定几何流形的几何不变量的有用的代数表达式。最近，人们对Cartan几何在最重要的背景下的存在和基本性质有了透彻的了解，并将重点转移到利用Cartan联系来研究所讨论的几何上。研讨会的主要学术目标是(1)聚集目前在一系列几何和分析问题上研究Cartan几何的不同研究人员，以及(2)向研究相同问题的研究人员介绍已产生有价值结果的Cartan几何技术。研讨会的主题与物理学有重要联系，包括广义相对论和ADS/CFT通信。这段时间与一个学期的“广义相对论动力学”课程重叠，组织者预计这两个活动的参与者之间将进行富有成效的互动。正在作出特别努力，邀请来自代表性不足群体或在发展中国家工作的早期职业研究人员和数学家。