This project aims to develop new methods to study systems of many interacting particles. An important application is concerned with the motion of electrons in molecules and solids both in out of equilibrium, such
as the response of electrons in a molecule or solid to a strong laser pulse. A common approach is to study these systems have relied on methods that treat the interaction between the particles as a perturbation
and the corresponding theory is called many-body perturbation theory. The method has had many successes but there are notable situations which are difficult to describe with current methods. We therefore aim to develop new methods which will be able to solve existing problems in the theory. The new approaches will be implemented in new numerical codes to study the properties of materials that were previously not accessible within the theory. Typical applications will involve the calculation of spectroscopic properties.