Number Theory: Hecke algebras for p-adic groups and the explicit local Langlands correspondence for G_2

 I will talk about my recent joint work with Aubert where we prove the local Langlands conjecture for G_2 (explicitly). This uses our earlier results on Hecke algebras attached to Bernstein components of reductive p-adic groups, as well as an expected property on cuspidal support, along with a list of characterizing properties. In particular, we obtain "mixed" L-packets containing F-singular supercuspidals and non-supercuspidals.