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Explore advanced mathematical concepts in this lecture focusing on conjugate actions in dimension 1 and their applications to deformation theory. Delve into the study of (semi-)conjugacy class closures of group actions on 1-manifolds, examining various mathematical aspects including small denominators, group orbit growth, distortion elements, bounded cohomology, and group orderability. Learn about key theoretical results such as C^1 smoothing through (semi-)conjugacies of small group actions and the associated C^2 and higher class obstructions. Examine the proof methodology behind the connectedness of Z^d actions space by diffeomorphisms with C^(1+ac) regularity, developed in collaboration with H. Eynard-Bontemps. Recorded during the "Foliations and Diffeomorphism Groups" thematic meeting at the Centre International de Rencontres Mathématiques in Marseille, France, this lecture features comprehensive chapter markers, keywords, abstracts, and bibliographies accessible through CIRM's Audiovisual Mathematics Library.
