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Explore a 90-minute mathematics lecture focusing on conjectures about families of maps on $\mathbb{P}^{N}$ as part of a series examining the geometry of preperiodic points for endomorphisms. Delve into a dynamical version of the "Relative Manin-Mumford" theorem, originally proven by Gao-Habegger for abelian varieties, and discover its connections to dynamical stability and various questions about moduli spaces of maps on $\mathbb{P}^{N}$. Learn from collaborative research presented by Laura DeMarco and Myrto Mavraki, recorded during the "Arithmetic, Algebraic and Analytics Dynamics" thematic meeting at the Centre International de Rencontres Mathématiques in Marseille, France. Access chapter markers, keywords, abstracts, bibliographies, and Mathematics Subject Classification through CIRM's Audiovisual Mathematics Library for enhanced learning experience.
