The canonical dimension: using the Bruhat-Tits building to investigate the wavefront set

An important invariant in the complex representation theory of reductive p-adic groups is the wavefront set, because it contains information about the character of such a representation. In my talk I will introduce a new invariant called the canonical dimension, which can be said to measure the size of a representation and which has a close relation to the wavefront set. I will then state some results I have obtained about the canonical dimensions of compactly induced representations and show how they teach us something new about the wavefront set. In the second part of my talk I sketch the proof of these results, which crucially uses the geometry of the Bruhat-Tits building. This illustrates a completely new approach to studying the wavefront set.