Ruijsenaars and Toda Integrable Systems

Watch a 57-minute lecture exploring the mathematical foundations and applications of Ruijsenaars and Toda integrable systems, delivered at the International Centre for Theoretical Sciences as part of a comprehensive program on discrete integrable systems. Delve into the connections between difference equations, cluster algebras, and probabilistic models while examining exactly solvable systems with multiple conserved quantities. Learn how these discrete integrable systems emerge from various branches of theoretical physics and mathematics, including statistical physics, string theory, combinatorics, representation theory, geometry, and probability. Explore key topics like integrable difference equations, soliton solutions, singularity structures, cluster algebra frameworks, and their applications to geometric objects and mathematical physics. Understand the relationship between integrable probability, interacting particle systems, stochastic growth models, and tools from quantum integrable systems and symmetric functions theory.