Strongly-ordered infrared limits for subtraction counterterms from factorisation

After a brief introduction to the problem of subtraction of infrared
divergences for high-order collider observables, we present a preliminary study
of strongly-ordered soft and collinear multiple radiation from the point of
view of factorisation. We show that the matrix elements of fields and Wilson
lines that describe soft and collinear radiation in factorised scattering
amplitudes can be re-factorised in strongly-ordered limits, providing a
systematic method to compute them, to characterise their singularity structure,
and to build local subtraction counterterms for strongly-ordered
configurations. Our results provide tools for a detailed organisation of
subtraction algorithms, in principle to all orders in perturbation theory.