%0 Journal Article %T A KAM result on compact Lie groups %A Livia Corsi %A Emanuele Haus %A Michela Procesi %J Mathematics %D 2014 %I arXiv %X We describe some recent results on existence of quasi-periodic solutions of Hamiltonian PDEs on compact manifolds. We prove a linear stability result for the non-linear Schr\"odinger equation in the case of $SU(2)$ and $SO(3)$. %U http://arxiv.org/abs/1411.0293v1