Recent progress in the calculation of the N3LO splitting functions

The four-loop DGLAP splitting functions, which govern the scale evolution of the Parton Distribution Functions (PDFs), are of the missing ingredients to push the frontier of QCD calculations to N3LO accuracy, as required to match the experimental precision at the LHC and at the forthcoming EIC. In this talk, I will report on the recent progress in the determination of the splitting functions from the direct calculation of a fixed number of moments of these quantities. This approach allows to control the evolution of the PDFs to percent-level precision over the relevant range of momentum fraction x.