  We study non-equilibrium dynamics of ultracold two-component Fermi gases in
low-dimensional geometries after the interactions are quenched from weakly
interacting to strongly interacting regime. We develop a T-matrix formalism
that takes into account the interplay between Pauli blocking and tight
confinement in low-dimensional geometries. We employ our formalism to study the
formation of molecules in quasi-two-dimensional Fermi gases near Feshbach
resonance and show that the rate at which molecules form depends strongly on
the transverse confinement. Furthermore, Pauli blocking gives rise to a sizable
correction to the binding energy of molecules.
