  We study the quench dynamics of a two-component ultracold Fermi gas from the
weak into the strong interaction regime, where the short time dynamics are
governed by the exponential growth rate of unstable collective modes. We obtain
an effective interaction that takes into account both Pauli blocking and the
energy dependence of the scattering amplitude near a Feshbach resonance. Using
this interaction we analyze the competing instabilities towards Stoner
ferromagnetism and pairing.
