Explore recent advancements in the theory of completely integrable nonlinear dispersive partial differential equations in this seminar presented by Monica Visan from the University of California, Los Angeles. Delve into key topics such as a priori bounds, orbital stability of multisolitons, well-posedness at optimal regularity, and the existence of dynamics for Gibbs distributed initial data. Gain insights into the fundamental objects connecting these diverse results and the varied approaches required for each problem. This hour-long presentation, titled "Determinants, Commuting Flows, and Recent Progress on Completely Integrable Systems," offers a comprehensive survey of cutting-edge developments in the field of PDE analysis and methods.