The Arakelov-Zhang pairing and Julia sets Andrew Bridy, Yale University Host: John Doyle Contact John Doyle (john.r.doyle@okstate.edu) for the Zoom link.
Abstract: The Arakelov-Zhang pairing is a measure of a "dynamical distance" between two rational maps defined over a number field K. The definition is fairly technical in terms of local analysis on Berkovich space, but the pairing has many nice properties that can be understood without invoking Berkovich space. We obtain a simple expression for the important case of the pairing with a power map, which may be interpreted as a limiting height of generic preimages. The expression is in terms of integrals over Julia sets; under certain disjointness conditions on Julia sets, it simplifies to a single canonical height term (in general, this term is a lower bound). This is joint work with Matt Larson.
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