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Explore the fascinating interplay between dynamics, algebra, and geometry in free-by-cyclic groups in this 48-minute lecture by Jean Pierre Mutanguha. Delve into the construction of semi-direct products of finitely generated free groups and integers, examining their Cayley graphs and other geometric models. Investigate the dynamics of defining automorphisms, algebraic properties of free-by-cyclic groups, and the coarse geometry of their models. Drawing inspiration from Thurston's work on surface homeomorphisms and 3-manifolds, gain insights into various results ranging from classic to recent developments. Discover key concepts and methodologies in this incomplete survey, and leave with a wealth of open problems to explore further in the field of geometric group theory.
