Recent years have seen impressive progress on the combination of next-to-next-to-leading-order (NNLO) calculations and parton showers for processes of high phenomenological interest. However, as state-of-the-art parton showers typically fail to match the singularity structure of NNLO calculations, these methods do not provide the same level of theoretical control as fully-differential matching schemes that are available at next-to-leading order (NLO).
In this talk, I will outline a new technique for the fully-differential matching of final-state parton showers to NNLO calculations, focusing on the simplest case of leptonic collisions with two final-state jets. The strategy is facilitated by working in the antenna formalism, making use of NNLO antenna subtraction on the fixed-order side and the sector-antenna framework on the shower side. I will present the implementation of all required components in the VINCIA antenna shower in PYTHIA 8.3 and discuss the generalisation to processes involving initial-state partons.