Workshop Recent Advances in Geometric Group Theory

本提案的目标是于2011年6月29日至7月1日在南安普顿大学举办为期三天的研讨会。几何群论是一个广阔的数学领域，它结合了代数，分析，几何和拓扑学的思想，并对所有这些学科做出了重要贡献。自M.格罗莫夫的开创性工作，介绍了双曲空间，双曲和相对双曲群的概念，发展了他们的理论，并展示了潜在的应用。自然，几何群论的主要主题之一就是研究这种“非正曲”群。其他学科，开始独立发展，但现在构成了重要组成部分的几何群论是Teichmueller理论和它的类似物在Culler-Vogtmann空间，小消去理论，粗几何，研究立方体复杂和解析群论。一些领先的专家在该地区已经给予初步协议出席并发言的研讨会。讲习班的目的是激发与会者之间的讨论，以促进这一令人兴奋的领域的进一步研究。参与者在职业生涯的早期阶段（博士学位。学生和博士后）将有一个极好的机会学习几何群论中各种主题的最新方法和技术。

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.