EXC 2044 - T04: Groups and actions

Basic data for this project

Description

The study of symmetry and space through the medium of groups and their actions has long been a central theme in modern mathematics, indeed one that cuts across a wide spectrum of research within the Cluster. There are two main constellations of activity in the Cluster that coalesce around groups and dynamics as basic objects of study, and these are captured in the three research units collected here. Units "Groups, dynamics and C*-algebras" and "Entropy, probability and geometry of groups" both focus on aspects of groups and dynamics grounded in measure and topology in their most abstract sense. This research treats infinite discrete groups as geometric or combinatorial objects and employs tools from functional analysis, probability, and combinatorics. The unit "Algebraic groups and Lie groups" examines, in contrast to abstract or discrete groups, groups with additional structure that naturally arise in algebraic and differential geometry.