Scalar Curvature: Structure and Regularity – Part 2/2

  • Speaker: Robin Neumayer
  • Time: 2:00-3:00
  • Abstract: A broad theme in geometric analysis aims to understand the geometric structure of Riemannian manifolds that satisfy constraints on curvature. Over the past 25 years, a rather complete picture has been given for the structure and a priori regularity of Riemannian manifolds with lower bounds on Ricci curvature, as well as their limit spaces. On the other hand, when one assumes only a lower bound on scalar curvature, the trace of the Ricci curvature, the situation is much less well understood. The scalar curvature asymptotically governs the volumes of balls of small radii, and arises in various settings in general relativity and differential geometry. This mini-course will focus on the structure and regularity of Riemannian manifolds with scalar curvature lower bounds.