Event Type:

Department Colloquium

Date/Time:

Tuesday, January 5, 2016 - 14:00 to 15:00

Location:

Kidder 364

Guest Speaker:

Institution:

University of South Florida

Abstract:

Groups acting on rooted trees by automorphisms play an important role in the modern group theory. The most famous examples of such groups lie in the class of groups generated by automata (or self-similar groups) and provide the simplest counterexamples to several important problems, such as Burnside problem on infinite finitely generated periodic groups, Day problem on amenability, and Strong Atiyah conjecture on L2-Betti numbers. In the last problem a crucial role was played by the so-called lamplighter group, the wreath product of (the countable product of copies of) Z_2 by the infinite cyclic group.

As a natural generalization of the lamplighter type groups we introduce the class of automorphisms of rooted d-regular trees, arising from affine actions on their boundaries viewed as infinite dimensional vector spaces. We build the automata defining these automorphisms and apply the developed techniques to completely describe the structure of a group generated by 4-state bireversible automaton that was beyond the reach of other known methods. This is a joint work with Said N. Sidki.

Host: