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In the Standard Model, many features of our the world around us are
believed to be a direct consequence of the Higgs sector. The LHC has
made amazing progress in exploring this sector, but critical
aspects are far from being established. One of the keys to future
progress is our ability to accurately simulate collisions across
disparate energy scales and to do so in a way that respects essential
physical properties such as positivity. To achieve this, we need to
learn how to combine the systematic accuracy of QFT with the
generality of physical parton showers.