What can modular flavour symmetries do for you?
João Penedo (INFN, Rome3)

In recent years, modular invariance has been applied to the SM flavour puzzle, yielding compelling results. In this string-inspired paradigm, one does not require a multitude of scalar fields (flavons) with aligned VEVs and complicated potentials. Taking a bottom-up approach, one may instead rely on a single complex field -- the modulus. Yukawa couplings and mass matrices are obtained from functions of its VEV, which can be the only source of flavour symmetry breaking and of CP violation. Such predictive modular setups may, among other things, shed light on the patterns of fermion mixing, the origin of fermion mass hierarchies and the strong CP problem.