Lie Groups, Representations and Discrete Mathematics

We will show how self-similar groups H(k) generated by finite automata can be related to Hanoi Tower games on k=3,4,... pegs. Then we will consider the spectrum of a Schreier graph of Hanoi Group H(3), will show that the group is of branch type, and will finish our talk with a discussion of the growth of diameters of finite Schreier graphs related to Hanoi groups and to other self-similar groups and how this growth reflect expanding properties. The amenability will appear in some moment as well.