Title: Small Scale Index Theory, Scalar Curvature, and Gromov’s Simplicial Norm

Speaker: Qiaochu Ma, Texas A&M & CUNY

Abstract: Scalar curvature encodes the volume information of small geodesic balls within a Riemannian manifold, making it, to some extent, the weakest curvature invariant. This raises a natural question: what topological constraints does scalar curvature impose on manifolds? In this talk, we shall show that for a manifold with a scalar curvature lower bound, the simplicial norm of certain characteristic classes can be controlled by its scalar curvature, volume, and injectivity radius of the universal covering. This is joint work with Guoliang Yu.