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Explore the intricacies of heat and Schrödinger evolution on degenerate Riemannian structures in this comprehensive lecture delivered by Ugo Boscain from Université Pierre et Marie Curie, Paris, France. Delve into advanced mathematical concepts as part of the School and Workshop on Mixing and Control series. Gain insights into the complex interplay between heat transfer and quantum mechanics in the context of degenerate Riemannian geometries over the course of this hour-long presentation.