Explore a 48-minute conference talk on the well-posedness of the derivative nonlinear Schrödinger equation on the line. Delve into the critical space analysis of this completely integrable and L^2-critical model, focusing on recent advancements in understanding its behavior below H^(1/2). Learn about the proof of well-posedness in the critical space on the line and discover the key results that contributed to this resolution. Gain insights from the collaborative work of Maria Ntekoume, Benjamin Harrop-Griffiths, Rowan Killip, and Monica Visan presented at the CRM Analysis Seminar.