Learn about skew RSK dynamics in this 57-minute lecture presented by Tomohiro Sasamoto at the International Centre for Theoretical Sciences. Explore discrete integrable systems through the lens of difference equations, cluster algebras, and probabilistic models. Delve into the properties of integrable systems, their exact solvability, and conserved quantities while understanding their role in non-integrable model analysis. Examine three key research areas: integrable difference equations and their soliton solutions, cluster algebra structures in discrete integrable systems, and integrable probability including interacting particle systems and stochastic growth models. Part of a comprehensive program featuring mini-courses, problem sessions, and workshop components, this lecture contributes to the broader discussion of discrete integrable systems and their applications in theoretical physics and mathematics.