William Rowan Hamilton Geometry and Topology Workshop

摘要奖：DMS-0846968首席研究员：Martin Bridgeman，Noel Brady，陶力该奖项支持美国演讲者和受邀的美国初级研究人员主持第四届William Rowan哈密尔顿几何和拓扑研讨会，该研讨会为期3天，将于2008年8月28-30日在爱尔兰都柏林的汉密尔顿数学研究所举行。研讨会的参与者包括来自低维拓扑、几何群论和双曲几何领域的顶尖研究人员、初级研究人员和研究生，他们对Heegaard分裂、映射类群和曲线复数相关的问题特别感兴趣。具体主题包括Heegaard分裂的组合数据与流形上的双曲结构的关系以及曲线复数上的Masur-Minsky技巧在曲面子群猜想和虚拟Haken猜想中的应用。在Heegaard分裂、绘制类群和曲线复合体的每个领域中，研究人员使用其他两个领域的技术的趋势已经越来越大。这个工作坊应该增加这一点，并将集中精力在共同的主题上。研究低维拓扑学、几何群论和双曲几何的数学家关心对称性的本质。例如雪花的对称性，建筑中的薄片图案，墙纸和瓷砖图案，以及化学中晶体或晶格结构的对称性。该奖项将使来自美国的顶尖研究人员、毕业生和初级研究人员与来自世界各地的研究人员聚集在一起，以结合方法和技术进行进一步的研究。这项活动将有助于聚焦下一代研究人员的研究计划，并将加深我们对对称性本质的理解。这项活动支持正在进行的国际研讨会，致力于在美国数学界和欧洲社区的一个新兴数学研究所(汉密尔顿数学研究所)之间建立联系。

AbstractAward: DMS-0846968Principal Investigator: Martin Bridgeman, Noel Brady, Tao LiThe award supports US speakers and invited US junior researchersattending the fourth William Rowan Hamilton Geometry and TopologyWorkshop, a 3-day, directed workshop to be held at the HamiltonMathematics Institute in Dublin, Ireland in August 28-30,2008. Participants at the workshop include leading researchers,junior researchers and graduate students from the fields of lowdimensional topology, geometric group theory, and hyperbolicgeometry who have a special interest in problems related toHeegaard splittings, mapping class groups, and curve complexes.Specific topics include the relation of the combinatorial data ofa Heegaard splitting to the hyperbolic structure on the manifoldand applications of Masur-Minsky techniques on the curve complexto the Surface Subgroup Conjecture and the Virtually HakenConjecture. There is already a growing tendency for researchersin each of areas of Heegaard splittings, mapping class groups,and curve complexes to use techniques from the other twoareas. This workshop should increase this, and will focuscollective energies on common themes.Mathematicians who study low dimensional topology, geometricgroup theory, and hyperbolic geometry are concerned about thenature of symmetry. Examples include the symmetries of asnowflake, frieze patterns in architecture, wallpaper and tilingpatterns, and symmetries of crystal or lattice structures inchemistry. This award will enable leading researchers, graduatestudents and junior researchers from the US to gather togetherwith researchers from around the world in order to combinemethods and techniques to further research. This activity willhelp focus the research programs of the next generation ofresearchers, and will deepen our understanding of the nature ofsymmetry. This activity supports an ongoing internationalworkshop dedicated to forging bonds between the US mathematicscommunity and an emerging mathematics institute (the HamiltonMathematics Institute) in the European community.