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Explore advanced mathematical research in this conference talk examining the Dynamical Schinzel-Zassenhaus Conjecture and its connection to transfinite diameter theory. Learn about Dimitrov's 2019 proof of the Schinzel-Zassenhaus Conjecture and discover how Habegger and Schmidt extended this strategy to address dynamical variants of the conjecture. Understand the role of Dubinin's Theorem on the transfinite diameter of hedgehogs, which are star-shaped trees in the plane, as a crucial tool in both results. Delve into ongoing research that establishes new upper bounds for the transfinite diameter of finite topological trees constructed using Hubbard trees of postcritically finite polynomials, which reflect their dynamical properties. Examine how these theoretical advances lead to practical applications in proving lower bounds for the Call-Silverman (canonical) height for specific classes of postcritically finite polynomials. Gain insights into cutting-edge developments in algebraic number theory, complex dynamics, and their intersection through this detailed mathematical exposition presented by Philipp Habegger from the University of Basel at the Institut des Hautes Etudes Scientifiques.
