Werner Ballmann

I will discuss relations between the geometry of spaces and groups that act on them. The main assumptions on the action are proper discontinuity and uniformness – these notions will be explained in the talk.

I will start with examples, e.g. tori and surfaces, related to Euclidean and hy- perbolic geometry. In the second part of the talk I will discuss properties of a group which follow from the structure of the space on which they act. The emphasis is on non-compact spaces and infinite groups.