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Explore advanced mathematical research in this lecture examining the intersection of algebraic geometry and arithmetic dynamics. Delve into joint work with Mavraki investigating arithmetic intersection numbers of sections of elliptic surfaces defined over number fields, which led to a Bogomolov-type extension and new proof of a theorem by Barroero and Capuano addressing aspects of the Zilber Pink conjectures. Discover the underlying geometric features of this mathematical problem and examine related open questions about families of maps and dynamical systems on the projective line P¹. Learn how elliptic surfaces connect to equidistribution phenomena and bifurcation theory in the context of arithmetic and algebraic geometry. Gain insights into cutting-edge research at the intersection of number theory, algebraic geometry, and dynamical systems from a leading expert in the field.
