International Centre for Theoretical Sciences, Bangalore, India

该奖项将用于支持来自美国机构的参与者参加2012年12月3日至16日在印度班加罗尔塔塔研究所国际理论科学中心举行的高级学校和关于群体、几何和动力学的讨论会议。特别考虑的领域包括：洛伦兹几何，负曲线空间的几何，离散群的几何，双曲流形的算术，李群中的格，实和复Kleinan群的几何和动力学，以及齐次空间上的流。这次高级学校和讨论会议的目的是向年轻的数学家介绍该领域的基础，他们的主要发展，以及用于他们研究的工具。几十年来，对不同空间上的离散群体作用的研究一直是一个重要的研究领域，起源于20世纪初H.Poincare的开创性工作。对复直线上某些微分方程解的研究引出了Fuchsian群和Kleinan群的概念，它们是黎曼球面的自同构离散群，也是二维和三维双曲几何的等距。对复杂空间上这些类型的离散群作用的研究，以及它们在高维和其他几何上的推广，仍然是当前研究的丰富来源。这次高级学校和讨论会议将促进这些领域的互动和促进研究，并将解释新一代geometers.http://www.icts.res.in/program/GGD2012在这些领域前沿的核心问题

This award will be used to support participants from US institutions attending an Advanced School and Discussion Meeting on Groups, Geometry and Dynamics at the International Centre for Theoretical Sciences at the Tata Institute in Bangalore, India during December 3-16, 2012. Special areas of consideration include: Lorentzian geometry, geometry of negatively curved spaces, geometry of discrete groups, arithmetic of hyperbolic manifolds, lattices in Lie groups, geometry and dynamics of real and complex Kleinian groups, and flows on homogeneous spaces. The aim of this Advanced School and Discussion Meeting is to introduce young mathematicians to the foundations of the fields, their major developments, and the tools used for their study.The study of discrete group actions on various spaces been an important area of research for many decades, originating in the pioneering work of H. Poincare in the early 20th Century. The study of of solutions of certain differential equations on the complex line led to the concept of Fuchsian and Kleinian groups, which are discrete groups of automorphisms of the Riemann sphere, also acting as isometries of hyperbolic geometries in two and three dimensions. The study of these types of discrete group actions on complex spaces, and their generalizations to higher dimensions and to other geometries, continues to be a rich source of current research. This Advanced School and Discussion Meeting will foster interaction and promote research in these areas, and will explain the core problems at the frontiers of these fields a new generation of geometers.http://www.icts.res.in/program/GGD2012