  Using a functional renormalization group approach we study the zero
temperature phase diagram of two-dimensional Bose-Fermi mixtures of ultra-cold
atoms in optical lattices, in the limit when the velocity of bosonic condensate
fluctuations are much larger than the Fermi velocity.
  For spin-1/2 fermions we obtain a phase diagram, which shows a competition of
pairing phases of various orbital symmetry ($s$, $p$, and $d$) and
antiferromagnetic order. We determine the value of the gaps of various phases
close to half-filling, and identify subdominant orders as well as short-range
fluctuations from the RG flow. For spinless fermions we find that p-wave
pairing dominates the phase diagram.
