William Rowan Hamilton Geometry and Topology Workshop

DMS 0624240。马丁·布里奇曼(PI)Noel Brady(共同PI)该奖项支持参加2006年9月在爱尔兰都柏林汉密尔顿数学研究所举行的第二届William Rowan Hamilton几何和拓扑研讨会的美国青年参与者。研讨会的参与者包括来自绘图班组、3-流形和几何群论领域的顶尖研究人员、初级研究人员和研究生。这将是一个为期3天的有指导的研讨会，重点是低维拓扑和几何群论中表面子群的无处不在的问题。具体的主题包括映射类群中纯伪Anosov曲面的存在性，以及单端Gromov双曲群和3-流形群中闭双曲面群的存在性。这三个领域的研究人员都越来越倾向于使用其他两个领域的技术。这个工作坊应该增加这种技术的交叉授粉，并将集中集体的精力在共同的主题上。研究群论的数学家关心对称性的本质。例如雪花的对称性，建筑中的浮雕图案，墙纸和瓷砖图案，以及化学中晶体或晶格结构的对称性。这一奖项将使来自美国的研究生和初级研究人员能够与来自世界各地的顶尖研究人员聚集在一起，以调查双曲曲面群(与埃舍尔“圆极限”绘图相关的对称)在数学中出现的其他对称群中的普遍存在。这项活动将有助于聚焦下一代几何群论家的研究计划，并将加深我们对对称性本质的理解。这项活动是美国数学界与欧洲共同体新兴数学研究所(汉密尔顿数学研究所)建立联系的第一步。

DMS 0624240. Martin Bridgeman (PI).Noel Brady (co-PI) The award supports junior US participants attending the secondWilliam Rowan Hamilton Geometry and Topology Workshop to be heldat the Hamilton Mathematics Institute in Dublin, Ireland in September 2006. Participants at the workshop include leading researchers, junior researchers and graduate students from the fields of mapping class groups, 3-manifolds and geometric group theory. This will be a 3-day, directed workshop focused on the question of the ubiquity of surface subgroups in low-dimensional topology and geometric group theory. Specific topics include the existence of purely pseudo-Anosov surfaces in mapping class groups, and the existence of closed hyperbolic surface groups in one-ended Gromov hyperbolic groups and in 3-manifold groups. There is already a growing tendency for researchers in each of these three areas to use techniques from the other two areas. This workshop should increase this cross-pollination of techniques, and will focus collective energies on common themes.Mathematicians who study group theory are concerned about the nature ofsymmetry. Examples include the symmetries of a snowflake, frieze patterns in architecture, wallpaper and tiling patterns, and symmetries of crystal or lattice structures in chemistry. This award will enable graduate students and junior researchers from the US to gather together with leading researchers from around the world in order to investigate the ubiquity of hyperbolic surface groups (symmetries associated to the Escher "circle limit" drawings) inside other symmetry groups that arise in mathematics. This activity will help focus the research programs of the next generation of geometric group theorists, and will deepen our understanding of the nature of symmetry. This activity is one of the first steps towards forging bonds between the US mathematics community and an emerging mathematics institute (the Hamilton Mathematics Institute) in the European community.