Charmonium production at mid-rapidity in Pb-Pb and p-Pb collisions with ALICE

We present an overview of the ALICE measurements on the production of $\mathrm{J}\mathrm{/}\psi$ in Pb-Pb collisions at a centre-of-mass energy per nucleon pair of $\sqrt{s_{\mathrm{N}\mathrm{N}}}=2.76\mathrm{T}\mathrm{e}\mathrm{V}$ and p-Pb collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=5.02\mathrm{T}\mathrm{e}\mathrm{V}$ at mid-rapidity ($|y_$\mathrm{l}\mathrm{a}\mathrm{b}$ | < 0.8$) down to zero transverse momentum. The cold nuclear matter effects estimated from the p-Pb measurements and their impact on the interpretation of Pb-Pb results are discussed, based on comparison of data to model calculations.