Reviews some recent applications of the gradient flow; shows that the short-flow-time matching coefficients are exact within an operator product expansion; illustrates the automatic decoupling of heavy quarks in the gradient-flow scheme of the strong coupling.

We develop a perturbative approach to the Ricci flow and use it to define a renormalization scheme for Newton's coupling.

We provide more details to the letter-style article on the calculation of bag parameters for heavy-meson lifetimes. We also apply the same method to heavy-meson mixing.

Combining lattice data with the perturbative matching coefficient, we calculate bag parameters for heavy-meason lifetime predictions. More details are provided in the accompanying longer article.

The gradient-flow coupling in QED is just the Laplace transform of the regular photon polarization function. Among other things, this paper studies the renormalization group structure of three-dimensional QED in this scheme.