Event Type:

Graduate Student Summer Seminar

Date/Time:

Wednesday, July 12, 2017 - 14:30 to 15:30

Location:

Kidder 364

Abstract:

A polynomial f(x) with rational coefficients induces

a self-map from the set of algebraic numbers to itself, and thus

determines a discrete dynamical system. Given a rational base

point b, the Galois groups of the splitting fields of the

polynomials f^n(x)-b are determined by the backward orbit

of b under repeated iteration of f in this dynamical system.

We examine the structure of these Galois groups. In particular,

we describe them using arboreal representations, i.e., their

realizations as groups of tree automorphisms. We then survey

some results and open questions in this field (pun intended).

This talk should be accessible to anyone who is familiar with

the introductory definitions and concepts of Galois Theory.