RNMS: Geometric Structures and Representation Varieties

RNMS：几何结构和表示种类

• 批准号: 1107367
• 负责人: William Goldman
• 金额: $ 151.14万
• 依托单位: University of Maryland, College Park
• 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 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1107367&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研究网络。 几何结构和表示簇 (GEAR) 网络涵盖了具有不同领域背景的数学家，例如经典 Teichmüller 理论、李群的离散子群、3 流形拓扑、调和映射、动力学以及希格斯丛的模空间和规范理论。近年来，这些领域的研究人员集中在围绕有限生成群表示的流形和模空间上的局部同质结构的常见问题上。一个领域的新技术和新工具带动了另一领域的进步，而相反的观点则凸显了新的问题。 GEAR 网络的目标是促进思想从一个领域到另一个领域的交叉授粉，建立一个超越当前部门的研究社区，培训学生和研究人员跨越传统界限，并通过这些方式推进网络目标的数学发展。该网络的主要项目包括不同地点的研究人员之间的访问和交流、旨在弥合目标专业之间差距或解决具体问题的专题会议和研讨会、帮助建立共同研究社区的全网络务虚会、研究生实习和暑期研究经验以及网络网络活动。该网络节点遍布美国、加拿大和欧洲的 46 个地点，覆盖范围广泛的机构，其中包括一些研究资源水平历史较低的机构。这些节点分布在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枢纽周围，其中主要枢纽位于厄巴纳-香槟分校。GEAR 研究网络主页：http://www.gear.math.illinois.edu