Explore a 24-minute IEEE conference talk on twin-width and its applications in tractable first-order model checking. Delve into concepts such as trigraphs, contraction sequences, unit intervals, and ktman graphs. Learn about Hamiltonian paths, bounded twin-width graph formula checking, and interpretations. Discover the role of magnetic stability in FO model checking and understand the dynamic programming approach used in this context. Gain insights from authors Idouard Bonnet, Eun Jung Kim, Stiphan Thomassi, and Rimi Watrigant from LIP, ENS Lyon, and LAMSADE, Paris-Dauphine University.