Advanced School and Workshops on Discrete Groups in Complex Geometry

复几何中离散群的研究起源于H.庞加莱在世纪初，研究了某些微分方程在复直线上的解。这导致了Fuchsian和Kleinian群的概念：它们是黎曼球面自同构的离散群。这与双曲几何密切相关，其中Fuchsian和Kleinian群是双曲二维和三维空间的等距群。对复空间上这些类型的离散群作用的研究，以及它们对高维和其他几何的推广，几十年来在复几何和全纯动力学中发挥了重要作用。这将是第一次会议，汇集工人在全纯动力学领域，高维复杂的Kleinian群，和变形理论的几何结构的流形。这个学校和研讨会的目的是介绍年轻的数学家的基础领域，它的一些主要发展和工具用于其研究。会议将从基础课程开始，为理论提供基础。然后，高级课程和研讨会将引导参与者到复杂几何当前研究的一些重要领域。 在研讨会结束时，一个问题会议将解决这些领域的未来方向。这次会议将汇集来自世界各地不同但相关领域的研究人员。 研究生和博士后特别将受益于暑期学校提供的迷你课程。 将优先考虑研究生，年轻的研究人员，代表性不足的群体和数学家没有其他可用的资金。在参与国际理论物理中心和欧洲的第三世界国家工作的研究人员将有机会与来自美国的同行进行交流。

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.