Recent progress in many-electron QED calculations of highly charged ions

In the talk I will present the recent advances in rigorous many-electron quantum electrodynamics calculations of various spectroscopic properties of highly charged ions, such as the binding energies, the hyperfine structure, and the g factor. I will also report about our recent study of the nuclear polarization effect in highly charged ions. It has been demonstrated that the nuclear-polarization contributions can be substantially canceled simultaneously by the rigid nuclear corrections. This opens an opportunity to test strong-field QED with a higher accuracy than expected before.