Inverse problems, real-time dynamics and lattice simulations

The determination of real-time dynamics of strongly coupled quantum fields is a central goal of modern nuclear and particle physics, which requires insight into quantum field theory beyond the weak-coupling approximation. While lattice QCD has provided vital insights into the non-perturbative static properties of quarks and gluons it hides their real-time dynamics behind an ill-posed inverse problem. In this proceeding I will discuss developments in tackling the inverse problem on the lattice and touch upon progress in the direct simualtion of real-time dynamics.Comment: 11 pages, 4 figures, plenary talk given at the XVth Quark confinement and the Hadron spectrum conference, August 1st - 6th, 2022, Stavanger, Norwa