Collaborative Number Theory Seminar at the CUNY Graduate CenterCoorganizers: Gautam Chinta, Brooke Feigon, Krzysztof Klosin,
Maria Sabitova,
Lucien Szpiro. Fall 2016 Schedule:September 30: Thomas J. Tucker (University of Rochester) Title: Towards a finite index conjecture for iterated Galois groups. Abstract: Let f be a polynomial over a global field. Let G denote the inverse limits of the Galois groups of f^n, where f^n denotes the nth iterate of n. Boston and Jones have suggested that under reasonable hypotheses, one might hope that G has finite index in the full group of automorphisms on an infinite tree corresponding to roots of iterates f^n. We will show that such a conjecture holds for cubic polynomials in characteristic 0, assuming certain wellknown diophantine conjectures. We will also suggest a more general finite index conjecture.
