for this workshop

## The Galois theory of orbits in arithmetic dynamics

at the

American Institute of Mathematics, San Jose, California

organized by

Rafe Jones, Michelle Manes, and Joseph Silverman

This workshop, sponsored by AIM and the NSF, will be devoted to the study of Galois properties of points in orbits of algebraic maps.

The main topics for the workshop are:

- "Arboreal" Galois groups of fields generated by points in backward orbits of finite algebraic maps.
- "Dynatomic" Galois groups of fields generated by periodic points of finite algebraic maps.

Arboreal Galois groups sit naturally as subgroups of tree (or graph) automorphism groups, while dynatomic Galois groups are naturally subgroups of certain wreath products. A fundamental problem is to determine general conditions under which these dynamically generated Galois groups have finite index in the natural geometric groups that contain them. This is a dynamical analog of Serre's theorem on the size of the Galois groups generated by torsion points on elliptic curves. The goal of the workshop is to better understand these towers of Galois groups over number fields and over function field in both the one-dimensional and higher dimensional settings. For the latter, an initial goal is to give a geometric characterization of those maps for which one does not expect a finite index theorem to hold, analogous to the case of CM elliptic curves.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email *workshops@aimath.org*