Deriving the Deligne-Langlands correspondence

Affine Hecke algebras and their representations play an important role in the representation theory of p-adic groups since they classify smooth representations generated by Iwahori-fixed vectors. The Deligne-Langlands correspondence, which was proved by Kazhdan and Lusztig, parametrises these representations by geometric data on the Langlands dual group. This talk is supposed to be a gentle introduction to this topic. I will also briefly talk about how this correspondence can be lifted to the derived level.