Advanced School and Workshops on Discrete Groups in Complex Geometry

复杂几何离散群高级学校和研讨会

• 批准号: 1010995
• 负责人: William Goldman
• 金额: $ 1.54万
• 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: 2010
• 资助国家: 美国
• 起止时间: 2010-06-01 至 2012-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1010995&HistoricalAwards=false
• 关键词: Advanced; Workshops; Discrete; Groups; Complex

The study of discrete groups in complex geometry originates in the pioneering work of H. Poincare in the early 20th Century, studying solutions of certain differential equations on the complex line. This led to the concept of Fuchsian and Kleinian groups: these are discrete groups of automorphisms of the Riemann sphere. This turns out to be closely related to hyperbolic geometry, where Fuchsian and Kleinian groups are groups of isometries of hyperbolic two and three dimensional spaces. The study of these types of discrete group-actions on complex spaces, and their generalizations to higher dimensions and to other geometries, has played for decades a major role in complex geometry and in holomorphic dynamics. This will be the first conference to bring together workers in the fields of holomorphic dynamics, higher dimensional complex Kleinian groups, and the deformation theory of geometric structures on manifolds.The aim of this School and Workshop is to introduce young mathematicians to the foundations of the field, some of its major developments and tools used for its study. The meeting will start with elementary courses to provide the foundations of the theory. Then advanced courses and a workshop will lead the participants to some of the important areas of current research in complex geometry. At the end of the workshop a problem session will address the future directions of these fields. This meeting will bring together researchers in diverse, but related areas, from all over the world. Graduate students and postdocs especially will benefit from the minicourses being offered in the summer school. Priority will be given to graduate students, young researchers, under-represented groups and mathematicians with no other available funding. Researchers working in the third world countries involved in ICTP and Europe will have a chance to interact with their counterparts from America.

复杂几何形状中离散组的研究起源于20世纪初期的H. poincare的开创性工作，研究了复杂线上某些微分方程的解决方案。这导致了紫红色和克莱恩群体的概念：这些是黎曼球体的自动形态的离散群体。事实证明，这与双曲线几何形状密切相关，紫红色和克莱尼亚组是双曲线两个和三维空间的异构体组。对复杂空间上的这些类型的离散群体行动的研究，以及它们对更高维度和其他几何形状的概括，在复杂的几何形状和霍明型动力学中发挥了几十年的主要作用。这将是第一次将霍明态动力学领域的工人，更高维度复杂的克莱尼人群体以及几何结构的变形理论汇集到歧管上的会议。该学校和研讨会的目的是将年轻的数学家介绍给该领域的基础，其中一些主要的开发项目和研究的一些工具。会议将从基础课程开始，以提供理论的基础。然后，高级课程和研讨会将使参与者进入复杂几何学研究的当前研究的一些重要领域。 在研讨会结束时，问题会议将解决这些领域的未来方向。这次会议将使来自世界各地的不同但相关领域的研究人员聚集在一起。 尤其是研究生和博士后，将从暑期学校提供的微型赛中受益。 没有其他可用资金的研究生，年轻研究人员，代表性不足的团体和数学家将优先考虑。在ICTP和欧洲参与的第三世界国家工作的研究人员将有机会与美国的同行互动。