Photon spectroscopies in correlated materials in and out of equilibrium

Photon-based spectroscopies have had a significant impact on both fundamental science and applications by providing an efficient approach to investigate the microscopic physics of materials. Together with the development of synchrotron X-ray techniques, theoretical understanding of the spectroscopies themselves and the underlying physics that they reveal has progressed through advances in numerical methods and scientific computing. In this talk, I will provide an overview of theories for angle-resolved photoemission spectroscopy and resonant inelastic X-ray scattering applied to quantum materials. First, I will discuss methods for studying equilibrium spectroscopies, including first-principles approaches, numerical many-body methods and a few analytical advances. Second, I assess the recent development of ultrafast techniques for out-of-equilibrium spectroscopies, from characterizing equilibrium properties to generating transient or metastable states, mainly from a theoretical point of view. Finally, I will identify the main challenges and provide an outlook for the future direction of the field.