Rudolf Zeidler (University of Münster)
We will discuss situations where a lower bound on the scalar curvature of a Riemannian manifold leads to a quantitative distance estimate as well as corresponding rigidity results. The study of these has been prompted by several recent conjectures of Gromov. Intuitively, these results can be seen as analogues for scalar curvature of classical comparison geometry statements such as the Bonnet-Myers theorem for Ricci curvature. However, unlike classical comparison geometry involving stronger curvature conditions, such results for scalar curvature typically rely on an additional topological assumption such as the non-existence of positive scalar curvature metrics on certain submanifolds. Therefore we will also provide an introduction to obstructions to the existence of positive scalar curvature metrics on closed manifolds.
