Abstract:

Do you long for a coordinate-free approach to Riemannian geometry? Are you filled with dread whenever your metrics develop singularities? Or can you not imagine why anyone would want to leave the world of smoothly varying tensors? Either way, come to this talk and discover Alexandrov spaces! This is a class of spaces that naturally generalises Riemannian manifolds, but in which curvature is defined purely in terms of triangles. We will see that many familiar Riemannian results still hold here. And if time permits, we will explore how these techniques from Alexandrov geometry can be used to control singular behaviour in my field of study, polyhedral manifolds.