Workshop Recent Advances in Geometric Group Theory

这项提议的目标是于2011年6月29日至7月1日在南安普顿大学组织一次为期三天的研讨会。几何群论是一个广泛的数学领域，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。在M.Gromov的开创性工作中引入了双曲空间、双曲群和相对双曲群的概念，发展了它们的理论并展示了它们的潜在应用之后，这一领域在过去的20年里得到了迅速的发展。当然，几何群论的一个主要主题就是研究这种“非正曲线”群。其他开始独立发展，但现在构成几何群论的重要组成部分的学科有：卡勒-伏格特曼空间中的Teichmueller理论及其类似物、小消去理论、粗几何、立方体复形的研究和分析群论。该领域的一些主要专家已经初步同意出席研讨会并发表演讲。讲习班的目的是促进与会者之间的讨论，以促进这一令人兴奋的领域的进一步研究。处于职业生涯早期阶段的学员(博士生和博士后)将有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.