Top-quark cross sections and distributions at aN³LO

We present theoretical predictions for top-quark total cross sections and for differential distributions in top-quark transverse momentum and rapidity. Third-order soft gluon corrections are added to the complete NNLO quantities to provide approximate N$^3$LO (aN$^3$LO) results, and electroweak corrections at NLO are also included. We calculate the theoretical uncertainties from scale dependence and from parton distribution functions in the proton, and estimate their impact on the total and differential cross sections. The higher-order corrections are large and they reduce the scale uncertainties. The results presented in this work include the best current theoretical input and are in good agreement with recent data from the LHC.