Groups and Dynamics Seminar

Date: September 20, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Volodymyr Nekrashevych, Texas A&M

Title: Amenability of iterated monodromy groups for some complex rational functions

Abstract: It is an open question if iterated monodromy groups of complex rational functions are amenable. Another open question is if groups generated by automat of polynomial activity growth are amenable. We prove that if the iterated monodromy group of a complex rational function is generated by an automaton of polynomial activity growth, then the group is amenable. At first, we show that orbital Schreier graphs of iterated monodromy groups are recurrent, by comparing the random walk on the graph with the Brownian motion on the associated Riemanian surfaces, Then we prove amenability of the group using techniques of extensive amenability. This is a joint work with K. Pilgrim and D. Thurston.