This research project proposes exploring fundamental aspects about the asymptotic structure of the spacetimes and its remarkable link with integrable systems in three-dimensional gravity in vacuum and coupled to matter fields. This surprising connection raises a number of interesting questions to be explored in the context of soliton theory that can be completely geometrized from the point of view of gravitation, as well as about its role in the contexts of dual field theories. This research proposal is based on recent results and has the plan to explore this deep relation in diverse setups involving soliton theory, black holes physics, conformal field theories, and thermalization theorem, among others.
