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Explore the intricate connections between dynamics, algebra, and geometry in free-by-cyclic groups in this 55-minute lecture by Jean Pierre Mutanguha. Delve into the construction of semi-direct products from automorphisms of finitely generated free groups and their integers. Examine the Cayley graph and other geometric models of these finitely generated free-by-cyclic groups. Investigate the interplay between the dynamics of defining automorphisms, algebraic properties of free-by-cyclic groups, and coarse geometry of geometric models. Learn how Thurston's work on surface homeomorphisms and 3-manifolds has influenced these concepts. Gain insights into various results, from classic to recent, and understand the key ideas behind them. Discover numerous open problems in this field for further exploration and research.
