Final Report Summary - UPFERMI (Unconventional pairing in ultracold Fermi gases) In the ERC project we have studied superfluidity and quantum magnetism in strongly interacting Fermi gases. Our experiments have revealed the collective Higgs mode in a strongly interacting Fermi superfluid and its disappearance when approaching the limit of tightly bound pairs (the BEC limit of superfluidity). The apparent stability of the Higgs mode even for strong interaction has been surprising since theoretical predictions existed only for the BCS regime. Moreover, we have studied repulsively interacting fermions on an optical lattice and we have devised measurement schemes to resolve the ordering of the spins into anti-ferromagnetic domains. This work, together with our complimentary investigations of the thermodynamics of the Hubbard model, highlight the ability of ultracold atoms in optical lattices as quantum simulators for problems from condensed matter physics.