Collaborative Number Theory Seminar at the CUNY Graduate Center

Co-organizers: Gautam Chinta, Brooke Feigon, Krzysztof Klosin, Maria Sabitova, Lucien Szpiro.

The seminar currently meets Fridays 3:00 to 4:30 PM in Room 3209. The CUNY Graduate Center is located on Fifth Avenue, on the east side of the street, between 34th and 35th Streets in midtown Manhattan. For further information, please contact Maria Sabitova.

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.