Explore a mathematical lecture presenting a recent proof of the soliton resolution conjecture for the Benjamin-Ono equation, delivered by Patrick Gerard from Université Paris-Saclay. Learn about the fundamental concept that the soliton resolution conjecture claims every solution to a dispersive equation decouples in long time asymptotics as a sum of soliton solutions plus a radiative remainder. Discover the collaborative research conducted with Louise Gassot and Peter Miller that successfully proves this conjecture specifically for the Benjamin-Ono equation. Gain insights into advanced mathematical concepts in dispersive equations, soliton theory, and asymptotic analysis through this comprehensive academic presentation from the Institut des Hautes Etudes Scientifiques.