RNMS: Geometric Structures and Representation Varieties

RNMS：几何结构和表示种类

• 批准号: 1107263
• 负责人: Steven Kerckhoff
• 金额: $ 128.37万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-15 至 2022-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1107263&HistoricalAwards=false
• 关键词: RNMS; Geometric; Structures; Representation; Varieties

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

几何结构和表示品种（Gear）该奖项支持数学科学中的研究网络。几何结构和代表性品种（齿轮）网络涵盖了数学家，这些数学家在潜水区中具有背景，例如经典的Teichmüller理论，Lie组的离散子组，3-歧管拓扑，谐波图，动力学，动力学和Higgs Bundles捆绑和尺寸理论的模态空间。近年来，这些领域的研究人员融合了围绕当地均匀结构的常见问题，这些结构在最终产生的群体的表示形式的歧管和模量空间上。一个领域的新技术和工具导致了另一个领域的进步，对比的观点突出了新问题。齿轮网络的目标是刺激从一个领域到另一个领域的思想交叉授粉，以建立一个超越当前部门的研究社区，培训学生和研究人员越过传统界限，并通过这些方式推进网络针对的数学。该网络的主要计划包括不同地点研究人员之间的访问和交流，旨在弥合目标亚种之间的差距或解决特定问题，网络范围的务虚会，以帮助建立一个普通的研究社区，研究生的学生实习和夏季研究经验以及网络网络工作活动。该网络的节点遍布美国，加拿大和欧洲的46个地点，涵盖了广泛的机构，其中包括一些历史上较低的研究资源。 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