Geometry Seminar

A fundamental 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 space of Langlands parameters. An important invariant of the character (viewed as a distribution) is the wavefront set, a measure of its singularities. 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. I will describe some progress in establishing a precise connection along these lines for representations of p-adic groups. In particular, I plan to report on recent results with Hiraku Atobe (arXiv:2602.22504) on the wavefront set of Arthur packets of classical p-adic groups, obtained by combining endoscopy and a basic case of unipotent representations computed in previous work with Lucas Mason-Brown and Emile Okada.