Property RD (Rapid Decay) for A2 buildings

I Will discuss property RD concerning discrete groups and boundary representation for trees, and A2 buildings. After having introduced property RD, the notion of buildings together with the questions related to thèse notions, I will try to explain how the action of a discrete Group on the Furstenberg boundary of a tree or a A2 building gives new estimates for property RD. This Will provide a new dynamical point of view of important questions in this area.
Joint work in progress with Thang Nguyen.