College of Liberal Arts and Sciences

# Department of Mathematics

## Algebra Seminar

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Title: Images of Iterated Polynomials over Finite Fields
Speaker: Jamie Juul (Amherst College)
Time: Wednesday, October 25, 2017 at 11:15 am
Place: MONT 313Abstract: We discuss how to bound the size of the image of the $n$-th iterate of a polynomial over a finite field using results about arboreal Galois representations. The main term in this bound involves the fixed point proportion of the Galois group of the field extension of $\mathbb{F}_q(t)$ obtained by adjoining all pre-images of the transcendental $t$ under the $n$-th iterate of the polynomial. We give explicit bounds on the fixed point proportion of the group in a general case.

Organizer: Liang Xiao