In 2019, Dimitrov proved the Schinzel-Zassenhaus Conjecture. Harry Schmidt and I extended his general strategy to cover initial first dynamical variants of this conjecture. One common tool in both results is Dubinin's Theorem on the transfinite diameter of a hedgehog, which is a star-shaped tree in the plane.
In this talk, I will report on joint work in progress with Schmidt. We find new...
In joint work with Mavraki a few years ago, we studied the arithmetic intersection numbers of sections of elliptic surfaces, defined over number fields. One consequence was a Bogomolov-type extension (and new proof) of a theorem of Barroero and Capuano, addressing a case of the Zilber Pink conjectures. I will describe the underlying geometric features of this problem and formulate related...
