On CAT(0) spaces and their applications
by
Miroslav Bacak
University of Newcastle

In this talk we focus on CAT(0) spaces (metric spaces with non-positive curvature), which have attracted and keep attracting a great deal of attention. This class of spaces contains Hilbert spaces, classical hyperbolic spaces, certain Riemannian manifolds, etc. We aim at introducing a new (weak) topology on CAT(0) spaces. This topology corresponds to a well-known type of (weak) convergence, and is of interest in Metric Fixed Point Theory.

We also recall some applications of CAT(0) spaces outside maths. In particular, Billera-Holmes-Vogtmann's construction of the Tree Space, which is reputed revolutionary in Phylogenomics. Furthermore, we will mention the concept of State Complex by Ghrist and Peterson, which plays an important role in Robotics.

Date received: January 4, 2010