College of Liberal Arts and Sciences

# Department of Mathematics

## Algebra Seminar

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Title: Some recent results on arboreal Galois groups [POSTPONED]
Speaker: Robert Benedetto (Amherst College)
Time: Wednesday, January 17, 2018 at 11:15 am
Place: MONT 313Abstract: Let $K$ be a number field, let $f\in K(x)$ be a rational function of degree $d$, and let $a\in K$. The roots of $f^n(z)-a$ are the $n$-th preimages of $a$ under $f$, and they have the natural structure of a $d$-ary rooted tree $T$. There is a natural Galois action on the tree, inducing a representation of the absolute Galois group of $K$ in the automorphism group of $T$. In many cases, it is expected that the image of this arboreal Galois representation has finite index in the automorphism group, but in some cases, such as when f is postcritically finite (PCF), the image is known to have infinite index. In this talk, I'll describe some recent results on arboreal Galois groups of certain polynomials, in both the PCF and non-PCF cases.Comments: This talk has been canceled due to weather and will be rescheduled later.

Organizer: Liang Xiao