Date:	Tue, October 27, 2015
Time:	14:15
Place:	Research I Seminar Room

Abstract: Iterated monodromy group (IMG) is a self-similar group associated to every branched covering f of the 2-sphere (in particularly to every rational map). It was observed that even very simple maps generate groups with complicated structure and exotic properties which are hard to find among groups defined by more "classical" methods. For instance, \(\operatorname{IMG}(z^2+i)\) is a group of intermediate growth and \(\operatorname{IMG}(z^2-1)\) is an amenable group of exponential growth. Unfortunately, we still face a lack of general theory which would unify and explain these nice examples.

In the talk I will first make a detour to the theory of growth of groups and overview the current status of studies of algebraic properties of IMGs. Then I will concentrate on two specific motivating examples of Thurston maps and prove that their IMGs have exponential growth (which is a very brand new result of mine obtained in Jyvaskyla). The remaining part of the talk will be open for a discussion towards the further research.