Student Dynamics Seminar

In many geometric setups with an essence of `non-positive curvature', it is possible to classify and study the geometries based on a notion of `rank'. The intuition is that `higher rank' imposes lots of symmetries on spaces, thus leading to `rigidity'. The talk will try to make this philosophy precise for some specific classes of geometries. We will discuss Ballmann and Burns-Spatzier's rank rigidity theorem for Riemannian non-positive curvature. We will also discuss the case of Hilbert geometries: a notion of rank in this setup (due to the speaker) and a rank rigidity theorem (due to A. Zimmer).  Speaker(s): Mitul Islam (UM)