Mishchenko–Fomenko subalgebras for centralizers and affine W-algebras

Let L be the centralizer of a nilpotent element in a finite dimensional semisimple Lie algebra. In my talk, based on a joint work with Arakawa, I will explain how to lift Mishchenko-Fomenko subalgebras of S(L) to commutative subalgebras of U(L). The construction relies in a crucial way on affine W-algebras at the critical level.