Neutrino mass and mixing with modular symmetry.

This is a review article about neutrino mass and mixing and flavour model building strategies based on modular symmetry. After a brief survey of neutrino mass and lepton mixing, and various Majorana seesaw mechanisms, we construct and parameterise the lepton mixing matrix and summarise the latest global fits, before discussing the flavour problem of the Standard Model. We then introduce some simple patterns of lepton mixing, introduce family (or flavour) symmetries, and show how they may be applied to direct, semi-direct and tri-direct CP models, where the simple patterns of lepton mixing, or corrected versions of them, may be enforced by the full family symmetry or a part of it, leading to mixing sum rules.

Gravitational Waves and Proton Decay: Complementary Windows into Grand Unified Theories.

Proton decay is a smoking gun signature of grand unified theories (GUTs). Searches by Super-Kamiokande have resulted in stringent limits on the GUT symmetry-breaking scale. The large-scale multipurpose neutrino experiments DUNE, Hyper-Kamiokande, and JUNO will either discover proton decay or further push the symmetry-breaking scale above 10^{16}  GeV.

Neutrino mass and mixing with discrete symmetry.

This is a review paper about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing.