# Algebra/Number Theory Seminar

## An upper bound for image set sizes of iterated quadratic maps

George Grell, U Rochester

Wednesday, April 3rd, 2019
1:00 PM - 2:00 PM
Hylan 1106A

Let $f(x)$ be a quadratic rational map defined over the field $\mathbb{F}_q$. Then work of Pink (2013) and Juul, Kurlberg, Madhu, and Tucker (2015) classifies the possible Galois groups that arise from considering $f^n(x)-t$ over the function field $\mathbb{F}_q(t)$. For one class of Galois groups we describe the proportion of elements of with fixed points, and use a lesser known generalization of Burnside’s Lemma to show this is an upper bound across all classes. The Chebotarev Density Theorem translates this result to a bound on image set sizes.

Event contact: dinesh dot thakur at rochester dot edu