Seminar

To participate in this seminar, please register HERE.

Iterated monodromy group (IMG) is a self-similar group that is naturally associated to every postcritically-finite branched covering map of the 2-sphere (in particular, to every pcf rational map). The IMG encodes combinatorial information about the map and its dynamics in a computationally efficient way.

In the late 90’s it was observed that the (normalized) Schreier graphs of some self-similar groups converge in the Gromov-Hausdorff metric to certain fractal spaces. In particular, the Schreier graphs of the IMG’s converge to the Julia sets of the corresponding rational maps. This observation led to the notions of contracting self-similar groups and their limit spaces introduced by Nekrashevych. 

The goal of the talk will be to explain these concepts and to discuss how nice combinatorial models may simplify the relevant computations. 

This seminar is for postdocs and PhD students, and we kindly ask faculty not to attend.