What happens when gold nuclei, accelerated to about 90% of the speed of light, strike gold nuclei at rest? For an extremely short time, t~10^-23 seconds, states of matter at extreme temperatures (10^12 K) and densities (>280 Mt/cm^3) are produced. The microscopic properties of the strong-interaction matter under extreme conditions of temperature and density is a topic of great current interest. Despite 18 orders of magnitude difference in system size and time, the conditions present in heavy-ion collisions share great overlap with the conditions of the strong-interaction matter in neutron-star mergers. The possibility to form and explore in the laboratory strong-interaction matter under extreme conditions is truly fascinating. The Compressed Baryonic Matter (CBM) experiment at FAIR has the potential to discover the most prominent landmarks of the QCD phase diagram expected to exist at high net baryon densities. The measurement of comprehensive set of diagnostic probes offers the possibility to find signatures of exotic phases, and to discover the conjectured first order deconfinement phase transition and its critical endpoint. In this talk the referent will focus on relevant observables to study criticality, emissivity, vorticity and equation-of-state of baryon rich matter. Particular emphasis is put on rare probes which are not accessible by other experiments in this energy range.

Resonant inleastic X-ray scattering (RIXS) especially in the soft X-ray region has seen a tremendous increase in applicability and scientific insight over the recent years. This was largely enabled by progress in instrumentation and theoretical description. Now the time is ripe to apply RIXS to pressing problems and develop the technique further making full use of the capabilities of novel X-ray sources. In my talk, I will address three main themes from my research: 1. Time-resolved RIXS at free-electron lasers applied to relevant dynamic processes in chemistry (on surfaces, in liquids and in solid catalysts) 2. RIXS with micrometer spatial resolution to resolve domain dynamics in complex materials and on devices in-operando 3. Non-linear spectroscopies in the soft X-ray range to enhance information content and signal levels I will show and discuss experimental results from all research themes and point to future development directions.