EVENT DETAILS AND ABSTRACT

Title: Arboreal Dynamics
Speaker: Steve Hurder
Speaker Info: UIC
Brief Description: Part of Midwest Dynamics Conference
Special Note: Part of Midwest Dynamics Conference
Abstract:

An arboreal action is an action of a countable group G acting on a bounded-valence tree, preserving a basepoint, or root vertex. The action preserves the distance from the root, and so the levels of the vertices in the tree. The action is minimal if the action is transitive on each level. We assume that all actions are minimal. An arboreal action induces an action on the boundary ends of the tree, and this action is a minimal equicontinuous action on the Cantor set of ends.

Study of the dynamical properties of arboreal actions has applications to:

✼ Structure of Absolute Galois Groups

✼ Classification of Generalized Solenoids

✼ Renormalization and Abstract Commensurators

This talk will survey some recent results and applications of arboreal dynamics in joint works with Olga Lukina and Wouter van Limbeek.