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

这一NSF奖为美国数学家参加将于2016年5月23日至6月3日在意大利的里雅斯特ICTP举行的关于几何群论和低维拓扑：最新联系和进展的高级学校和研讨会提供部分支持。这项拟议的活动是一系列“热门话题”的混合，将为处于各个职业阶段的数学家提供巨大的互动和产生新想法的机会。这所高级学院将让研究生接触到一系列不同的研究课题。将美国学生和国际学生介绍给来自世界各地的顶尖专家，应该会对美国和发展中国家的数学培养产生深远影响。培养美国数学家和发展中国家数学家之间更紧密联系和互动的潜力是教师和学生的长期利益。这个高级学院和研讨会将涵盖的主要主题包括几何结构的特征变化和变形，双曲3-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和几乎特殊的立方体复形和群。最近在这些领域有了重要的发展，例如：几何群论在Wise的工作中的影响，以及随后Agol对3-流形拓扑中著名的“虚拟猜想”的解决。活动网址为：http://indico.ictp.it/event/7646/.

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/.