Date: Tuesday, January 20, 2009
Title: Polynomial mappings
Abstract: I will present properties of polynomials mappings and
generalizations. I will first describe all polynomials
f and g for which there is a complex number c such that
the orbits {c, f(c), f(f(c)), ...} and {c, g(c), g(g(c)), ...}
have infinite intersection. I will also discuss a common
generalization of this result and Mordell's conjecture
(Faltings' theorem). After this I will move to polynomial
mappings over finite fields, with connections to curves having
large automorphism groups and instances of a positive
characteristic analogue of Riemann's existence theorem.
Speaker: Michael Zieve
Institution: IAS, Princeton
