RNMS: Geometric Structures and Representation Varieties

几何结构和表现形式(齿轮)该奖项支持数学科学研究网络。几何结构和表示变体(GEAR)网络包括具有不同领域背景的数学家，如经典Teichmüler理论、李群的离散子群、3-流形拓扑、调和映射、动力学以及Higgs丛和规范理论的模空间。近年来，这些领域的研究人员集中在有限生成群表示的流形和模空间上的局部齐次结构周围聚集的常见问题上。一个领域的新技术和工具导致了另一个领域的进步，而截然不同的观点突出了新的问题。Gear网络的目标是促进思想从一个地区到另一个地区的交叉授粉，建立一个超越当前分歧的研究社区，培训学生和研究人员跨越传统界限，并通过这些手段推进网络所针对的数学。该网络的主要方案包括不同地点的研究人员之间的访问和交流，旨在弥合目标分专业之间差距或解决具体问题的重点会议和讲习班，全网务虚会，以帮助形成共同的研究社区，研究生实习和暑期研究经验，以及网络联网活动。该网络的节点分布在美国、加拿大和欧洲的46个地点，覆盖了广泛的机构，其中包括几个研究资源水平处于历史低位的机构。这些节点围绕伊利诺伊大学厄巴纳-香槟分校、马里兰大学和斯坦福大学的中心中心排列，主要枢纽在厄巴纳-香槟。Gear研究网络主页：http://www.gear.math.illinois.edu

GEometric structures And Representation varieties (GEAR)This award supports a Research Network in the Mathematical Sciences. The GEometric structures And Representation varieties (GEAR) network encompasses mathematicians with backgrounds in diverse areas such as classical Teichmüller theory, discrete subgroups of Lie groups, 3- manifold topology, harmonic maps, dynamics, and moduli spaces of Higgs bundles and gauge theory. In recent years researchers in these areas have converged on common problems clustered around locally homogeneous structures on manifolds and moduli spaces of representations of finitely generated groups. New techniques and tools in one area have led to advances in another, and the contrasting points of view have highlighted new questions. The goals of the GEAR network are to spur cross-pollination of ideas from one area to another, to build a research community transcending current divisions, to train students and researchers to cross traditional boundaries, and by these means to advance the mathematics targeted by the network. The main programs of the network include visits and exchanges among researchers at different locations, focused meetings and workshops designed to bridge gaps between targeted subspecialties or to address specific problems, network-wide retreats to help forge a common research community, graduate student internships and summer research experiences, and cyber-networking activities. Spread over 46 locations in the US, Canada and Europe, the nodes of the network cover a wide range of institutions, including several with historically low levels of resources for research. The nodes are arranged around central hubs at The University of Illinois at Urbana-Champaign, The University of Maryland, and Stanford University, with the lead hub in Urbana-Champaign.GEAR Research Network home page: http://www.gear.math.illinois.edu