Explore a lecture by Roman Sauer that proves a generalization of Gromov's main inequality between volume and simplicial volume, replacing the lower Ricci curvature bound with a macroscopic scalar curvature bound. This 1 hour 28 minute presentation from the Hausdorff Center for Mathematics details joint work with Sabine Braun that extends Guth's theorem from hyperbolic manifolds to arbitrary Riemannian manifolds. Learn about the quantitative version of this mathematical advancement more recently developed by Hannah Alpert, which is also covered in the talk.