William Rowan Hamilton Geometry and Topology Workshop; September 2009, Dublin, Ireland

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The award supports US speakers and invited US junior researchers attending the fifth William Rowan Hamilton Geometry and Topology Workshop, a 3-day, directed workshop on Computational and Algorithmic Geometry to be held at the Hamilton Mathematics Institute in Dublin, Ireland in September 17-19, 2009. 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 computational and algorithmic problems in geometry and topology. Specific topics include the structure of low-volume hyperbolic 3- manifolds and the theory of random manifolds. In low-volume hyperbolic 3-manifold theory Gabai-Meyerhoff-Milley introduced the Mom technology to study low volume hyperbolic manifolds. During the conference we will consider how far the techniques can be pushed to provide a clear picture of low volume hyperbolic manifolds. In geometric group theory, the workshop will consider the general role of curvature and combinatorics in decision problems. 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. Computers have become an integral tool in this study, both for proving new results as well as motivating new directions through experiment and calculation. 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 this 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.