### Mathematics Colloquium

# Kurt Falk

### (Universität Bremen)

## "Rough CAT(0) spaces"

** Date: ** |
Mon, November 12, 2012 |

** Time: ** |
17:15 |

** Place: ** |
Research II Lecture Hall |

**Abstract:** In the talk I will be discussing rough CAT(0) spaces, or rCAT(0) in short, introduced by Buckley and myself, in an attempt to unify CAT(0)-theory and Gromov hyperbolicity, with special emphasis on boundary theory. When defining the boundary of a rCAT(0) space, bouquets of short segments, a concept related to Vaisala's roads, replace the classical geodesic rays to infinity known from the definition of the ideal boundary of a metric space. However, rCAT(0) spaces come in three flavours of which only the strongest allows a meaningful boundary theory, and the weakest turns out to be already known as so-called bolic spaces. As of now, we do not know whether these three conditions are equivalent or not. In the last part of the talk I will discuss, time permitting, rCAT(0) groups.