William Rowan Hamilton Geometry and Topology Workshop

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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.