Gradient flow is a diffusion-like smearing transformation that smoothly suppresses short-distance ultraviolet fluctuations, thus introducing a simple non-perturbative method to renormalise strongly-coupled theories such as Quantum Chromodynamics (QCD). 

It has become an invaluable tool in lattice simulations of both QCD and theories beyond the Standard Model, providing a method for e.g. scale setting and the topological structure of the vacuum.

Many recent developments have identified the deep potential of the gradient flow as a renormalisation procedure, opening new methodologies to calculate running couplings, the renormalisation group beta function, and renormalised composite operators.

These applications often depend on perturbative calculations in the short-flow-time expansion to match the gradient flow to other renormalisation schemes and provide phenomenologically-relevant results, for observables such as the energy-momentum tensor, quark masses, and parton distribution functions.

This workshop will convene the leading experts on both the perturbative and non-perturbative aspects of gradient flow to tackle the current theoretical and computational challenges, and to chart the future directions of this growing field.