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Height pairings and preperiodic points in P^1

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Laura DeMarco
Northwestern University
Tue, 2018-07-03 15:00 - 15:50
MPIM Lecture Hall

In 2011, Matt Baker and I used height functions and arithmetic equidistribution 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, inspired by questions and conjectures about elliptic curves and their torsion points.  The key ingredient is an estimate on the Arakelov-Zhang intersection numbers in families of heights.  This is joint work with Holly Krieger and Hexi Ye.

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