Galois uniformity in quadratic dynamics over k(t)k(t)

TextWe prove that the arboreal Galois representation attached to a large class of quadratic polynomials defined over a field of rational functions k(t)k(t) in characteristic zero has finite index in the full automorphism group of the associated preimage tree. Moreover, we show that in most cases, the index is bounded independently of the polynomial.VideoFor a video summary of this paper, please visit http://youtu.be/loO7qn4ncWs.