Simplicial and asymptotical aspects of the holographic principle

In this thesis, we study some aspects of a possible holographic correspondence in two different systems: three dimensional Chern-Simons theory and asymptotically flat space-times. In the former we use simplicial techniques to study CS/WZW correspondence and in particular we construct the discretized WZW partition function for SU(2) group at level 1. In the latter we outline the main characteristics of a field theory living at null infinity invariant under the action of the asymptotic symmetry group: the BMS group. In particular, using fibre bundle techniques, we derive the covariant wave equations for fields carrying BMS representations in order to investigate the nature of boundary degrees of freedom.