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Explore a mathematical lecture examining uniform versions of the dynamical Bogomolov conjecture, a dynamical counterpart to the classical Bogomolov conjecture in algebraic geometry. Delve into the theoretical framework where polarized endomorphisms f : X → X of projective varieties and subvarieties Z ⊂ X, defined over number fields, are analyzed for their relationship between Zariski dense small sequences and preperiodic behavior under canonical height functions. Learn about collaborative research findings with Johan Taflin and Gabriel Vigny that establish several key results in this area, including a dynamical proof of a uniform version of a Bogomolov-type statement for algebraic tori. Gain insights into advanced topics in Diophantine approximation and transcendence theory through this specialized mathematical presentation delivered at the Centre International de Rencontres Mathématiques during their thematic meeting on Diophantine approximation and transcendence.
