Speaker:  Anne-Marie Aubert (IMJ, Paris)

Title:  Enhanced Langlands parameters and Hecke algebras

Abstract:  We will first explain how to construct a Galois analogue of the Bernstein decomposition of the category of smooth representations of p-adic reductive groups. The role of irreducible objects will be played by conjugacy classes of enhanced Langlands parameters. These latter are partitioned into series thanks to the generalized Springer correspondence, and each series is in bijection with the simple modules of a (possibly twisted) extended affine Hecke algebra. Next, guided by the work of Lusztig for unipotent representations of p-adic groups, we will apply this construction to build an explicit local Langlands correspondence in numerous situations.