Explore the concept of scalar curvature rigidity in manifolds through this 48-minute lecture by Thomas Schick from the University of Göttingen. Delve into the phenomenon where increasing scalar curvature necessitates shrinking the manifold, with a focus on round spheres as the first established example by Llarull using spinorial techniques. Examine known solutions, current research questions, and the broader implications of this geometric property in mathematics. Gain insights into the intricate relationship between scalar curvature and manifold structure in this advanced talk presented at the Institut des Hautes Etudes Scientifiques (IHES).