Conference: Groups, geometry and dynamics

Kervaire研讨会：群的几何2013（瑞士数学博士课程），Les diableets，瑞士，2013年3月10-15日。会议涵盖了现代群论的几个分支：几何群论、无限群的渐近行为、群作用和动力系统。研究一小时的讲座是由该领域的主要专家提供的几门迷你课程的补充。几何群论是一个相对年轻的领域，其根源在于组合群论和拓扑学。20世纪80年代中期，在Gromov思想的推动下，群论学家开始关注细胞复合体所携带的几何结构。这种关注极大地阐明了早期的组合和拓扑研究，并激发了其他正在迅速发展的创新思想。随着它在过去20年的发展，几何群论发展了许多不同的方面，包括几何，拓扑，分析，逻辑。无穷群的渐近行为问题自九十年代初以来一直是几何群论的主要研究课题之一。群的渐近不变量反映了群的大尺度几何，在理论和应用中都有重要的作用。群体行为与动力系统的相互作用是群论研究的一个新领域。一方面，共形动力系统产生了大量具有有趣的代数、几何和谱性质的群。另一方面，这样的群可以显示出具有显著的几何和测量理论规律性的共形动力系统。http://www.unige.ch/~tatiana/Diablerets/Diablerets/home.html

Kervaire Seminar: Geometry of groups 2013 (Swiss Doctoral Program in Mathematics), Les Diablerets, Switzerland, 10-15 March, 2013.The conference covers several branches of modern group theory: geometric group theory, asymptotic behavior of infinite groups, group actions and dynamical systems. Research one-hour talks are complemented by several mini-courses given by the leading experts in the field. Geometric group theory is a relatively young field with roots in combinatorial group theory and topology. In the mid 1980's, spurred by ideas of Gromov, group theorists began to pay attention to the geometric structures which cell complexes can carry. This attention shed a great deal of light on the earlier combinatorial and topological investigations and stimulated other innovative ideas which have been developing at a rapid pace. As it has grown over the past 20 years, geometric group theory has developed many different facets, including geometry, topology, analysis, logic. Asymptotic behavior of infinite groups has been one of the main themes in geometric group theory since the early nineties. The asymptotic invariants of a group reflect the large-scale geometry of the group, they paly an important part in theory and applications. Interplay between group actions and dynamical systems is a new area of group theory. On the one hand, conformal dynamical systems yield a rich source of such groups with interesting algebraic, geometric, and spectral properties. On the other hand, such groups can be shown to yield conformal dynamical systems with remarkable geometric and measure-theoretic regularity. http://www.unige.ch/~tatiana/Diablerets/Diablerets/home.html