International Centre for Theoretical Sciences, Bangalore, India

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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