Conformal symmetry breaking on differential forms and some applications

Rapid progress has been made recently on symmetry breaking operators for real reductive groups. Based on Program A-C for branching problems (T.Kobayashi [Progr.Math.2015]), we illustrate a scheme of the classification of (local and nonlocal) symmetry breaking operators by an example of conformal representations on differential forms on the model space $(X,Y)=(S^n, S^{n-1})$, which generalizes the scalar case (Kobayashi--Speh [Memoirs of Amer.Math.Soc. 2015]) and the case of local operators (Kobayashi--Kubo--Pevzner [Lecture Notes in Math. 2016]). Some applications to automorphic form theory, motivations from conformal geometry, and the methods of proof are also discussed.