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Explore a mathematical lecture that delves into the study of conjugate actions in dimension 1 and their applications to deformation theory. Learn about the complexities of (semi-)conjugacy classes of group actions on 1-manifolds, examining various aspects including small denominators, growth of groups and orbits, distortion elements, bounded cohomology, and group orderability. Discover general results on C^1 smoothing via (semi-)conjugacies of small group actions and understand the obstructions present in class C^2 and higher. Examine the proof concepts behind the connectedness of Z^d actions by diffeomorphisms with C^(1+ac) regularity, developed in collaboration with H. Eynard-Bontemps. Recorded during the thematic meeting "Foliations and Diffeomorphism Groups" at the Centre International de Rencontres Mathématiques in Marseille, France, this lecture includes chapter markers, keywords, abstracts, and bibliographies for enhanced learning accessibility.
