William Rowan Hamilton Geometry and Topology Workshop

奖项：dmd -0846968首席研究员：Martin Bridgeman， Noel Brady， Tao li该奖项支持美国演讲并邀请美国青年研究人员参加第四届William Rowan Hamilton几何和拓扑研讨会，该研讨会将于2008年8月28日至30日在爱尔兰都柏林的汉密尔顿数学研究所举行，为期3天。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主要研究人员、初级研究人员和研究生，他们对与heegard分裂、映射类群和曲线复合体相关的问题有特殊的兴趣。具体内容包括：heegard分裂的组合数据与流形上双曲结构的关系；曲线复形上的Masur-Minsky技术在曲面子群猜想和虚哈肯猜想中的应用。对于每一个领域的研究者来说，使用其他两个领域的技术，包括分裂、映射类群和曲线复合体，已经有了越来越大的趋势。这次讲习班应加强这一点，并将把集体精力集中在共同主题上。研究低维拓扑、几何群理论和双曲几何的数学家关注对称性的本质。例子包括雪花的对称性，建筑中的雕花图案，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主要研究人员、研究生和初级研究人员能够与来自世界各地的研究人员聚集在一起，以结合方法和技术来进一步研究。这项活动将有助于下一代研究人员的研究项目，并将加深我们对对称本质的理解。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新兴的数学研究所（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.