Title: An application of "Selmer group Chabauty" to arithmetic dynamics
Abstract:
The irreducibility or otherwise of iterates of polynomials is an
important question in arithmetic dynamics. For example, it is
conjectured that whenever the second iterate of x^2 + c (with c a
rational number) is irreducible over Q, then so are all iterates.
A sufficient criterion for the iterates to be irreducible can be
expressed in terms of rational points on certain hyperelliptic curves.
We will show how to use the "Selmer group Chabauty" method developed by
the speaker to determine the set of rational points on a hyperelliptic
curve of genus 7. This leads to a proof that the sixth iterate of x^2 +
c must be irreducible if the second iterate is.