Motivic homotopy theory and stable homotopy groups

Abstract: These notes, written version of a Bourbaki talk, survey Morel-Voevodsky's motivic homotopy theory over a field, with a focus on computations of motivic homotopy sheaves, both stable and unstable. We also describe Isaksen-Wang-Xu's applications to the determination of stable stems through the motivic Adams spectral sequence, which also paved the way toward synthetic homotopy theory.