William Rowan Hamilton Geometry and Topology Workshop

Boston College, Chestnut Hill MA

Investigators

Abstract

Abstract Award: DMS-0846968 Principal Investigator: Martin Bridgeman, Noel Brady, Tao Li The award supports US speakers and invited US junior researchers attending the fourth William Rowan Hamilton Geometry and Topology Workshop, a 3-day, directed workshop to be held at the Hamilton Mathematics 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 low dimensional topology, geometric group theory, and hyperbolic geometry who have a special interest in problems related to Heegaard splittings, mapping class groups, and curve complexes. Specific topics include the relation of the combinatorial data of a Heegaard splitting to the hyperbolic structure on the manifold and applications of Masur-Minsky techniques on the curve complex to the Surface Subgroup Conjecture and the Virtually Haken Conjecture. There is already a growing tendency for researchers in each of areas of Heegaard splittings, mapping class groups, and curve complexes to use techniques from the other two areas. This workshop should increase this, and will focus collective energies on common themes. Mathematicians who study low dimensional topology, geometric group theory, and hyperbolic geometry are concerned about the nature of symmetry. 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 leading researchers, graduate students and junior researchers from the US to gather together with researchers from around the world in order to combine methods and techniques to further research. This activity will help focus the research programs of the next generation of researchers, and will deepen our understanding of the nature of symmetry. This activity supports an ongoing international workshop dedicated to forging bonds between the US mathematics community and an emerging mathematics institute (the Hamilton Mathematics Institute) in the European community.