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Explore the third lecture in a series on discrete integrable systems, focusing on Total Positivity, Directed Networks and Integrable Cluster Dynamics presented by Michael Gekhtman at the International Centre for Theoretical Sciences. Delve into advanced mathematical concepts as part of a comprehensive two-week program examining discrete integrable systems, difference equations, cluster algebras, and probabilistic models. Learn from expert discussions on exactly solvable systems and their conserved quantities, with particular emphasis on discrete systems emerging from theoretical physics and mathematics. Gain insights into 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. Participate in a program designed for both junior and senior researchers, featuring mini-courses, problem sessions, and workshop components, supported by international organizations including the Japanese Society for the Promotion of Science and the Centre National de la Recherche Scientifique.
