Collaborative Number Theory Seminar at the CUNY Graduate Center
Co-organizers: Gautam Chinta, Brooke Feigon, Krzysztof Klosin,
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 n-th 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 well-known diophantine conjectures. We will also suggest a more general finite index conjecture.