Weak corrections to Higgs hadroproduction in association with a top-quark pair

We present the calculation of the next-to-leading contribution of order ${\alpha }_S^2{\alpha }^2$ to the production of a Standard Model Higgs boson in association with a top-quark pair at hadron colliders. All effects of weak and QCD origin are included, whereas those of QED origin are ignored. We work in the MadGraph5_aMC@NLO framework, and discuss sample phenomenological applications at a 8, 13, and 100 TeV $pp$ collider, including the effects of the dominant next-to-leading QCD corrections of order ${\alpha }_S^3\alpha$.