Workshop Recent Advances in Geometric Group Theory

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.

Geometric Group Theory is presently one of the fastest developing areas of mathematics and its overall importance continuously increases due to the number of its applications to the other branches of mathematics, physics, computer science and biology. The impact of the workshop can be categorized into three main directions: research, education and applications. Research impact. The proposed workshop will bring together a number of prominent experts in the area of Geometric Group Theory to give scientific talks and participate in research discussions aimed at tackling some of the most important questions in the subject. The speakers will be asked to introduce the other participants to latest directions of their research and will also be encouraged to offer other problems for discussion. Resulting research will be published in leading mathematical journals and made available to free preprint archives like arxiv.org. We anticipate about 50 participants at the workshop, and plan to have 10-12 talks over three days which will be designed to allow plenty of time for research discussions and the development of new collaborations. Educational impact. This will amount to the transfer of knowledge and skills from the experts in the area to the participants of the workshop, in particular to the attending Ph.D. students and post-docs. We anticipate that a significant number of participants will be researchers at an early stage of their career, who will definitely benefit from meetings and discussions with more experienced colleagues. Applications. Several applications of Geometric Group Theory to sciences (other than Mathematics) have already been discovered are being thoroughly investigated. These include applications to the study of phylogenetic trees in Biology, solution of optimization and reconfiguration problems in Robotics, Biology and Computer Science, and group-based cryptography.