Workshop Recent Advances in Geometric Group Theory

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The goal of this proposal is to organise a three-day workshop at the University of Southampton from June 29th to July 1st, 2011. Geometric Group Theory is a vast area of Mathematics that combines ideas from Algebra, Analysis, Geometry and Topology and makes important contributions to all of these subjects. This area has been rapidly developing during the last 20 years, after M. Gromov'sseminal work, which introduced the concepts of hyperbolic spaces, hyperbolic and relatively hyperbolic groups, developed their theories and demonstrated the potential applications. Naturally, one of the principal themes of Geometric Group Theory is the study of such `non-positively curved' groups. Other subjects, which started to develop independently, but which now constitute importantparts of Geometric Group Theory are Teichmueller Theory and its analogue in Culler-Vogtmann Space, Small Cancellation Theory, Coarse Geometry, the study of Cube Complexes and Analytic Group Theory.Some of the leading experts in the area have already given preliminary agreements to attend and speak on the workshop. The workshop will aim to stimulate discussions among its participants in order to promote further research in this exciting area. The participants at early career stages (Ph. D. students and post-docs) will have an excellent opportunity to learn the latest methods and techniques in a variety of topics within Geometric Group Theory.