The first part of this talk is about the local Langlands correspondence. This is a correspondence between complex representations of a reductive group over a local field and representations of the Weil-Deligne group to the L-group of G. I will describe the so-called “Desideratum”, which are the expected properties of this correspondence that uniquely determine it, e.g., preservation of discreteness, Plancherel measures, Gamma factors, and Local intertwining relation.
