Polynomial mappings

Series: 
Job Candidate Talk
Wednesday, January 7, 2009 - 15:00
1 hour (actually 50 minutes)
Location: 
Skiles 255
,  
IAS
Organizer: 
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.