Improving predictions for associated $t\bar{t}H$ production at the LHC: soft gluon resummation through NNLL accuracy

In the following we present our recent results on the resummation of soft gluon corrections to the $pp\to t\bar{t}H$ cross section at the LHC. The resummation was carried out at next-to-next-to-leading-logarithmic (NNLL) accuracy using the Mellin space technique. Obtained results were matched to the NLO cross section. We show that the resummation leads to reduction of scale-variation uncertainty of the total $pp\to t\bar{t}H$ cross section.