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Learn about discrete integrable systems in this 58-minute lecture from the International Centre for Theoretical Sciences' program on difference equations, cluster algebras, and probabilistic models. Explore the relationship between Skew Column RSK Dynamics and the Box and Ball System through detailed mathematical analysis. Delve into key concepts of integrable systems, including their exact solvability properties and conserved quantities, while examining their connections to theoretical physics and mathematics. Discover how these systems relate to statistical physics, string theory, combinatorics, representation theory, geometry, and probability. Gain insights into ultradiscretization of equations, cellular automata, quantum groups, tropical geometry, and stochastic processes. Part of a comprehensive two-week program featuring mini-courses, problem sessions, and workshop components, this lecture contributes to the broader discussion of discrete integrable systems and their applications in modern mathematical physics.
