Colloquium: "Classification of Non-Random Rational Functions, with Applications"

Michael Zieve, University of Michigan

Abstract: I will describe all complex rational functions of one variable which, in a certain precise sense, behave differently than a random rational function of the same degree.  This is the culmination of a long series of papers by many authors going back to Zariski's thesis.  I will then present applications of this result to topics such as value distribution of meromorphic functions, classification of branching types of branched covers of surfaces, properties of orbits in complex and arithmetic dynamics, and generalizations of Mazur's theorem on uniform boundedness of rational torsion on elliptic curves.

Host: John Shareshian

Tea @ 3:45pm in Cupples I, room 200