Mitul Islam (MPI Leipzig)

Abstract: The (Hilbert metric) geometry of properly convex domains generalizes real hyperbolic geometry. This generalization is far from the Riemannian notion of non-positive curvature, but they share some intriguing similarities. I will explore this connection from a coarse geometry viewpoint. In this talk, I will focus on Morse geodesics, which are the coarsely “negatively-curved" directions. We will see that this "negative curvature" can be characterized entirely using linear algebraic data (singular values of matrices) or projective geometric data (regularity of boundary). This is joint work with Theodore Weisman.