Representation theory is the study of group actions on vector spaces. In this talk I will discuss the representation theory of a specific class of groups, called reductive p-adic groups. In particular I will introduce an interesting invariant of representations of these groups called the canonical dimension. There is a nice combinatorial geometric object attached to p-adic groups known as the Bruhat-Tits building. I will explain how we can use the geometry of this building to deduce a lower bound for the canonical dimension of representations of a p-adic group, thus showing what the geometry tells us about the representation theory.