Appears in collection : Not Only Scalar Curvature Seminar

There are three great domains in geometry, which lie on the boundary of "soft" and "rigid":

(1) low dimensional, especially 4-dimensional topology/geometry;
(2) symplectic topology/geometry; (3) scalar curvature bounded from below.

I will try to elucidate in my lecture common features of these three and explain the specificity of the problems arising with the scalar curvature.