Geometric Group Theory and Low-Dimensional Topology: Recent Connections and Advances

几何群论和低维拓扑：最新联系和进展

• 批准号: 1624301
• 负责人: Alan Reid
• 金额: $ 3万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-05-01 至 2017-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1624301&HistoricalAwards=false
• 关键词: Geometric; Group; Theory; Low; Dimensional

This NSF award provides partial support for U.S. based mathematicians to participate in an advanced school and workshop on "Geometric Group Theory and Low-Dimensional Topology: Recent Connections and Advances," to be held at ICTP, Trieste, Italy, 23 May - 3 June 2016. The proposed activity is a mix of "hot topics" that would afford tremendous opportunities to mathematicians at all career stages to interact and generate new ideas. The advanced school will expose graduate students to a diverse array research topics. Introducing both US based and international students to leading experts from across the globe should have a profound effect on cultivating mathematics in the US and in the developing world. The potential for fostering initial contacts and interactions that lead to closer connections between US based mathematicians and those in the developing world is a long term benefit for faculty and students.The main topics to be covered at this advanced school and workshop include character varieties and deformation of geometric structures, effective geometry and topology of hyperbolic 3-manifolds, left orderability and Heegaard Floer theory, the mapping class group action on Teichmuller space and the curve complex, dynamics on these spaces and virtually special cube complexes and groups. There have been important developments in these areas recently, for example: the impact of geometric group theory in the work of Wise and subsequently Agol's resolution of the famous "virtual conjectures" in 3-manifold topology. The event website is: http://indico.ictp.it/event/7646/.

该NSF奖项为美国数学家提供部分支持，以参加将于2016年5月23日至6月3日在意大利的里雅斯特国际理论物理中心举行的关于“几何群论和低维拓扑：最近的联系和进展”的高级学校和研讨会。拟议的活动是一个混合的“热门话题”，将提供巨大的机会，数学家在所有职业阶段的互动和产生新的想法。 高级学院将使研究生接触到各种各样的研究课题。 将美国和国际学生介绍给来自地球仪的顶尖专家，应该会对美国和发展中国家的数学培养产生深远的影响。促进美国数学家和发展中国家数学家之间的初步接触和互动的潜力是教师和学生的长期利益。这个高级学校和研讨会的主要议题包括几何结构的特征多样性和变形，双曲三维流形的有效几何和拓扑，左序性和Heegaard Floer理论，Teichmuller空间和曲线复形上的映射类群作用，这些空间上的动力学以及实际上特殊的立方体复形和群。有重要的发展，在这些领域最近，例如：影响几何群论的工作明智的，随后阿戈尔的决议著名的“虚拟aidentures”在3流形拓扑。活动网址：http://indico.ictp.it/event/7646/。