Complex dynamics and arithmetic equidistribution – Laura DeMarco – ICM2018

Dynamical Systems and Ordinary Differential Equations
Invited Lecture 9.5
Complex dynamics and arithmetic equidistribution
Laura DeMarco

Abstract: I will explain a notion of arithmetic equidistribution that has found application in the study of complex dynamical systems. It was first introduced about 20 years ago, by Szpiro–Ullmo–Zhang, to analyze the geometry and arithmetic of abelian varieties. In 2011, Matt Baker and I used the theory to show when two complex rational functions have only finitely many (pre-)periodic points in common. In this talk, I will explain how to obtain uniform bounds in families, and I will show how to use dynamical methods to return to the setting of abelian varieties.

ICM 2018 – International Congress of Mathematicians ©
 
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