The wavefront set of representations of reductive p-adic groups

A difficult question in the local Langlands framework is to understand the interplay between the characters of irreducible smooth representations of a reductive group over a local field and the geometry of the dual space of Langlands parameters. An important invariant of the character (viewed as a distribution, i.e, a continuous linear functional on the space of smooth compactly supported functions) is the wavefront set, a measure of its singularities along with their directions. Motivated by the work of Adams, Barbasch, and Vogan for real reductive groups, it is natural to expect that the wavefront set is dual (in a certain sense) to the geometric singular support of the Langlands parameter. Dan Ciubotaru will give an overview of these ideas and describe recent progress in establishing a precise connection for representations of reductive p-adic groups.