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Watch a mathematics lecture exploring polynomial automorphisms of affine space, focusing on the subgroup of tame automorphisms. Delve into fundamental questions about normal subgroups, Tits alternative, and dynamical degrees through the lens of metric spaces, specifically the coset and valuation complexes. Follow detailed examinations of Aut($\mathbb{A}^{2}$) = Tame($\mathbb{A}^{2}$), Tame($\mathbb{A}^{3}$), and Tame(Q($\mathbb{A}^{4}$)) cases, with the latter addressing tame automorphisms preserving nondegenerate quadratic forms. Recorded at the Centre International de Rencontres Mathématiques during the "Arithmetic, Algebraic and Analytics Dynamics" thematic meeting, access this comprehensive mathematical discussion through CIRM's Audiovisual Mathematics Library, complete with chapter markers, keywords, abstracts, and bibliographies for enhanced learning navigation.
