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Explore the second lecture in a three-part mathematics series focusing on degenerate integrability in Poisson quotients of Heisenberg doubles and their relationship to Ruijsenaars-Schneider systems. Delve into advanced mathematical concepts examining how integrable master systems on classical doubles inherit properties through reduction, with particular emphasis on the principal orbit type of Heisenberg doubles. Learn how these reduced systems connect to Ruijsenaars-Schneider (relativistic Calogero-Moser) type many-body systems with additional spin degrees of freedom. Part of the Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications" at the Erwin Schrödinger International Institute, this technical mathematics lecture builds upon the foundations established in the first talk about cotangent bundles and prepares for the final lecture's exploration of quasi-Poisson doubles.
