Focussing on the mathematics related to the recent proof of ergodicity of the (Weil–Petersson) geodesic flow on a nonpositively curved space whose points are

Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and

The interaction between ergodic theory and discrete groups has a long history and much work was done in this area by Hedlund, Hopf and Myrberg in the 1930s. The

Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.