Explore a General Relativity seminar presentation where Nikolaos Athanasiou from the University of Crete discusses semi-global existence and trapped surface formation in the Einstein-Yang-Mills system. Delve into the development of a novel gauge and scale invariant hierarchy of non-linear estimates for the Yang-Mills curvature, building upon An's "signature for decay rates" approach. Learn how these estimates, combined with gravitational degrees of freedom calculations, establish semi-global existence and lead to trapped surface formation through ODE arguments. Gain insights into this collaborative research work conducted with Puskar Mondal and Shing-Tung Yau, which advances our understanding of complex gravitational systems.