Gradient flow renormalization: from lattice QCD to the precision frontier

Gradient flow is a continuous smearing operation that can be interpreted as a real-space Wilsonian renormalization group transformation. As such, gradient flow can be used to predict the non-perturbative running of the QCD gauge coupling and quark masses using techniques from lattice quantum field theory. I report on recent efforts from the Fermilab Lattice and MILC collaborations targeting a sub-percent determination of the strong coupling constant at the pole mass of the Z boson from lattice QCD simulations using gradient flow. I close off with a discussion of parallel efforts targeting MS-bar quark masses at 2 GeV using similar techniques.