Second order QCD corrections to the $g + g \rightarrow H + H$ four-point amplitude

In this contribution we compute the two loop massless QCD corrections to the four-point amplitude g + g → H + H . We work in the effective theory where the Higgs boson interact with gluons in the infinite top quark mass limit. Our calculation is an important ingredient to the third-order QCD corrections to Higgs boson pair production.