Towards NNLO QCD corrections to Higgs boson pair production

Higgs boson pair production plays an important role in the determination of the Higgs boson self coupling. The predictions based on next-to-leading order corrections show a large dependence on the renormalization scheme of the top quark mass, which requires a next-to-next-to-leading order calculation. We discuss the current status and show first results of the three-loop virtual corrections.