International Centre for Theoretical Sciences, Bangalore, India

该奖项将用于支持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关于群体、几何和动力学的高级学校和讨论会议。特殊领域的考虑包括：洛伦兹几何，几何的负弯曲空间，几何的离散群体，算术的双曲流形，格在李群，几何和动力学的真实的和复杂的Kleinian群，流齐次空间。这个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。彭加勒在世纪早期。对复线上某些微分方程解的研究导致了Fuchsian和Kleinian群的概念，它们是黎曼球面自同构的离散群，也可以作为二维和三维双曲几何的等距。对这些类型的离散群作用在复杂空间上的研究，以及它们对高维和其他几何的推广，仍然是当前研究的丰富来源。这个高级学校和讨论会议将促进互动，促进这些领域的研究，并将解释这些领域的前沿核心问题，新一代的geometers.http://www.icts.res.in/program/GGD2012

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