Despite the seeming flexibility of scalar curvature, many rigidity phenomena have been established which give some of the strongest insights into scalar curvature. Important examples include Geroch’s conjecture and Llarull’s theorem. In order to further understand scalar curvature, we ask corresponding geometric stability questions, where the hypotheses of the rigidity phenomenon are relaxed, and one would like to show that Riemannian manifolds which satisfy the relaxed conditions are close to the rigid objects in some topology. In this talk we will survey what is known for scalar curvature stability, discuss what some of the conjectures are in this area, and describe important tools which have been useful so far.

Zoom link: https://rochester.zoom.us/j/98580630084