juliette.COUTENS@univ-amu.frThe Langlands program consists of several deep conjectures linking two areas of mathematics via the study of reductive groups: number theory, and representation theory and harmonic analysis. Within this framework, Bernstein, Deligne and Kazhdan established a fundamental result known as trace Paley–Wiener theorem for reductive p-adic groups. It gives a characterization of the image of a certain transformation arising from the trace of certain representations.
The aim of this talk is to explain this trace Paley-Wiener theorem in the group case, and how to generalize this to a certain spherical variety. The study of harmonic analysis in this setting is part of what is now called the Relative Langlands program, whose goal is to extend the philosophy of Langlands from groups to homogeneous spaces.