  We calculate the equilibrium Josephson current through a disordered
interacting quantum dot described by a Sachdev-Ye-Kitaev model contacted by two
BCS superconductors. We show that, at zero temperature and at the conformal
limit, i.e. in the strong interacting limit, the Josephson current is
suppressed by $U$, the strength of the interaction, as $\ln(U)/U$ and becomes
universal, namely it gets independent on the superconducting pairing. At finite
temperature $T$, instead, it depends on the ratio between the gap $\Delta$ and
the temperature. A proximity effect exists but the self-energy corrections
induced by the coupling with the superconducting leads seem subleading as
compared to the self-energy due to the interaction for large number of
particles. Finally we compare the results of the original four-fermion model
with those obtained considering zero interaction, two-fermions and a
generalized q-fermion model.
