William Rowan Hamilton Geometry and Topology Workshop

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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.