The exchange of mass, energy, and metals between galaxies, their surrounding circum-galactic medium (CGM), and the gas permeating halos at larger scale represents a fundamental part of the modern astrophysics. Both components still elude our knowledge. Indeed, we are very far from having a census of the CGM properties in the bulk of the galaxy population. Furthermore, the halo gas is well known at large scale only in the most massive halos of our Universe, the galaxy clusters (intra-cluster medium, ICM), but it is still very elusive in the bulk of the virtualized halo population at the group mass scale (Intra-group medium IGrM).
For this reason, so far, the study of such baryon cycle has been linked almost exclusively to galaxy evolution in a so called "streetlight bias”. Albeit more difficult to detect, the IGrM and the CGM are the other two key players on the stage, and their evolution across cosmic time is linked to the baryon exchange as much as the galactic component. Due to the substantial lack of information on the nature of the CGM and IGrM at large scales, many key questions remain unanswered. For instance, how is the IGrM affected at large scales by the feedback imparted energy? In other words, how does the baryon cycle affect the large-scale structure of our Universe? How much energy, momentum and entropy are released to the still elusive CGM hot component around galaxies? What is the main mechanism of interplay between CGM and central galaxy?
With the advent of instrument such as eROSITA, XRISM and JWST, and the enormous variety of results collected by Alma, MUSE, KCWI and LOFAR, it is time to review the state of the art of this research field. The final goal of this workshop is to fill the knowledge gap and review in an unbiased way all the key aspects of the baryon cycle: from the hot IGrM enclosed in the bulk of the virtualized halo population, to the CGM at hundreds of kpc from the central galaxy, and down to the main mechanisms in act at the galaxy center able to trigger the baryonic exchange.