Charm Production at RHIC and LHC to $O({\alpha }_s^3)$

We present results on rapidity and transverse momentum distributions of inclusive charm quark production in hadronic and heavy-ion collisions at RHIC and LHC energies, including the next-to-leading order, $O({\alpha }_s^3)$, radiative corrections and the nuclear shadowing effect. We determine hadronic and nuclear K-factor for the differential and total inclusive cross sections for the charm production. We discuss theoretical uncertainties inherent in our calculation. In particular, we find that different extrapolations of gluon density to low-$x$ region introduce large theoretical uncertainty in the calculation of charm production at LHC energies. Finally, we comment on the possibility of detecting the quark-gluon plasma signal as an enhanced charm production in heavy-ion collisions at RHIC.