Aspects of susy CFTs, multiplets and deformations, and 6d SCFTs.

I will discuss work with Cordova and Dumitrescu.  We systematically analyze the possible operator content of unitary superconformal multiplets in  three, and higher, spacetime dimensions.  There is a surprisingly rich and exotic zoo of multiplets, and sporadic phenomena.  As applications, we classify supersymmetry preserving deformations, the absolutely protected multiplets, and the conserved currents or free fields that can appear in superconformal theories.  I will also discuss earlier work on the 6d a-theorem for supersymmetric theories, and some recent extensions.