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This lecture, the third in a series, explores the Minimal Model Program for foliations presented by Calum Spicer at the Centre International de Rencontres Mathématiques. Delve into how the classification framework for algebraic varieties has been adapted to study foliations on projective surfaces, a concept pioneered by Brunella, Mendes, and McQuillan in the early 2000s. Learn about recent developments in minimal model theory for foliations on higher dimensional projective varieties, with special focus on three well-developed cases: rank one foliations, co-rank one foliations, and algebraically integrable foliations. Discover the concept of adjoint foliated structures, a recent innovation addressing unique challenges in applying minimal model techniques to foliations. This recording was captured during the thematic meeting "Foliations, birational geometry and applications" on February 6, 2024, in Marseille, France, and is available with chapter markers, keywords, abstracts, and bibliographies through CIRM's Audiovisual Mathematics Library.
