Mathematics has a wide range of different disciplines, from algebra to geometry and from analysis to topology, etc. Some discoveries, however, are able to link several disciplines together and open a field of interplay. Two of such recent discoveries are self-similar group representations and projective spectrum of linear operators. The goal of this workshop is bring together scholars in spectral theory, representation theory, complex dynamics and other related fields to exchange and examine some recent discoveries on self-similarity and projective spectrum.