CAT(0) spaces of higher rank

Contact: Stephan Stadler (stadler@mpim-bonn.mpg.de)

A Hadamard manifold – or more generally a CAT(0) space – is said to have higher
rank if every geodesic line lies in a flat plane. If a higher rank Hadamard manifold
admits finite volume quotients, then it has to be a symmetric space or split as a direct
product. This is the content of Ballmann’s celebrated Rank Rigidity Theorem, proved
in the 80s. It has been conjectured by Ballmann that his theorem generalizes to the
synthetic setting of CAT(0) spaces. In the talk I will discuss Ballmann’s conjecture
and report on recent progress.