Anna Wienhard: Beyond hyperbolic geometry

Euclidean geometry was already studied by the Greeks, but it took until the 19th century for hyperbolic geometry to be discovered. Since then hyperbolic geometry has been ubiquitous, for example in the classification of surfaces and of three manifolds; it even found applications in machine learning. Euclidean and hyperbolic geometry are just two examples of a much wider class of geometries of non-positive curvature. These non-positively curved geometries are often much more rigid, but combining them with hyperbolic groups opens up a completely new world in the study of Lie groups and their discrete subgroups. In the talk we will take a tour that leads us from hyperbolic geometry into this new world.