Rigidity and Uniformity in Algebraic Dynamics

Explore the fascinating intersection of algebraic dynamics and arithmetic geometry in this 45-minute talk by Hexi Ye at BIMSA. Delve into the study of endomorphisms of algebraic varieties and their connection to torsion points on abelian varieties. Discover how analyzing geometric configurations of preperiodic points led to groundbreaking collaborative research with Laura DeMarco and Holly Krieger, resulting in uniform upper bounds for torsion points on genus 2 curves in their Jacobians. Gain insights into the proof methods employed, including analytic and potential-theoretic tools, as well as the examination of degenerations in families of dynamical systems and non-archimedean dynamics. Learn about the talk's relevance to recent major breakthroughs, such as advancements in the uniform Manin-Mumford conjecture and its dynamical variants, providing a comprehensive overview of cutting-edge research in this field.