Signatures of Chaos and the structure of eigenstates in holography

The physics of quantum thermalisation and quantum chaos is crucial to our understanding of the properties of black holes in holography. In this talk I will give an overview of the chaotic behaviour of model holographic systems. I will specifically focus on the properties of their eigenstates with a view on a number of different manifestations of chaos, these being dynamical chaos à la Lyapunov, spectral chaos à la Wigner/Dyson and finally operator complexity à la Krylov.