Geometry and Algebra of Preperiodic Points in PN - Lecture 1

Explore the first lecture in a mathematical series examining conjectures about the geometry of preperiodic points for endomorphisms of $ \mathbb{P}^{N}$, focusing on the Dynamical ManinMumford Conjecture (DMM) formulated by Shouwu Zhang in the 1990s. Delve into the classification of subvarieties of $\mathbb{P}^{N}$ containing Zariski-dense sets of preperiodic points, building upon the foundation of the original Manin-Mumford Conjecture concerning torsion points in abelian varieties. Learn from joint work presented by Laura DeMarco and Myrto Mavraki, recorded during the thematic meeting on Arithmetic, Algebraic and Analytics Dynamics at the Centre International de Rencontres Mathématiques in Marseille, France. Access this mathematical content through CIRM's Audiovisual Mathematics Library, featuring chapter markers, keywords, enriched video content with abstracts and bibliographies, and comprehensive Mathematics Subject Classification for enhanced learning navigation.