Title: Non-equilibrium many-body physics of polaritons in atomic and solid-state media

Abstract: Hybrid light-matter excitations, so-called polaritons,
combine the advantages of photons in detection and transmission
with the interactions of their matter component. They are therefore
not only of great technological interest but also promising tools
to probe new states of matter. However, their driven and dissipative
nature also poses a challenge for any theoretical description.
In this talk I will explain how this challenge can be addressed
with non-equilibrium field-theory. Using two examples from my recent
research I will provide a small glimpse into the rich many-body
physics of polaritons. I will begin by introducing a systematic
expansion in the interaction range and leverage it to provide a
quantitative description of non-equilibrium phase transitions in
photonic waveguides. Subsequently I will address the time-evolution
of polaron-polaritons in a two-dimensional semiconductor irradiated
by an intense light pulse, highlighting our recent advances towards
the quantitative description of the dynamics of highly excited
many-body systems.