Self-similar groups: Aut(X*) and its subgroups

This lecture explores the self-similarity of groups, focusing on Aut(X*) and its subgroups. It covers tree automorphisms, sections, and the structure of self-similar groups like the Hanoi Towers group. The lecture delves into the concept of automaton groups, exponential growth, and the free monoid generated by specific elements. It also discusses the representation of tree automorphisms through portraits and the calculus of sections, emphasizing the interplay between Aut(X*) and the semigroup X*. The instructor provides insights into the unique actions and compositions within self-similar groups.