Unveiling the Galaxy Cluster - Cosmic Web Connection with X-ray observations in the Next Decade

In recent years, the outskirts of galaxy clusters have emerged as one of the new frontiers and unique laboratories for studying the growth of large scale structure in the universe. Modern cosmological hydrodynamical simulations make firm and testable predictions of the thermodynamic and chemical evolution of the X-ray emitting intracluster medium. However, recent X-ray and Sunyaev-Zeldovich effect observations have revealed enigmatic disagreements with theoretical predictions, which have motivated deeper investigations of a plethora of astrophysical processes operating in the virialization region in the cluster outskirts. Much of the physics of cluster outskirts is fundamentally different from that of cluster cores, which has been the main focus of X-ray cluster science over the past several decades. A next-generation X-ray telescope, equipped with sub-arcsecond spatial resolution over a large field of view along with a low and stable instrumental background, is required in order to reveal the full story of the growth of galaxy clusters and the cosmic web and their applications for cosmology.