Description 
We describe exact results and broad intuition at the interface of topology and superconductivity. We discuss briefly a rigorous upper bound on the superconducting transition temperature T_{c} in two dimensions that holds for arbitrary interaction strength, order parameter symmetry or pairing mechanism. This follows from an exact upper bound on superfluid stiffness largely controlled by the noninteracting physics, yet valid in any dimension and with arbitrary interactions. We demonstrate that this places stringent bounds on T_{c} in several strongly correlated systems of interest, in which estimating T_{c} is a notoriously hard problem. Another aspect of physics that is well understood in noninteracting and weak coupling systems is band topology. In an unrelated work, we show how ARPES matrix elements provide sharp signatures of topological band inversion in the normal state of an ironbased superconductor. In this material, an unusual interplay of spinorbit coupling and strong correlations results in topological inversion in a band with no observable dispersion. In another unrelated work, we show how understanding pairing within valleys in a simple lattice model leads to new intuition for intrinsic topological superconductivity in materials with valley degrees of freedom. We discuss its relevance for a wide variety of materials from transition metal dichalcogenides and antiperovskite oxides on the brink of a topological transition, to magic angle twisted bilayer graphene.
