LIE GROUPS, REPRESENTATIONS AND DISCRETE MATH | |

Topic: | Asymptotics and Spectra of Cayley and Schreier Graphs of Branch Groups |

Speaker: | Zoran Sunik |

Affiliation: | Texas A & M |

Date: | Tuesday, March 7 |

Time/Room: | 2:00pm - 3:15pm/S-101 |

We provide calculations of growth and spectra of Cayley and Schreier graphs related to some branch groups. Among the examples, we present a class of groups of intermediate growth defined by primitive polynomials over finite fields (the original Grigorchuk example fits in this setting as the group corresponding to the unique primitive polynomial x^2+x+1 over GF(2)) and the Hanoi Towers group on 3 pegs. In each case, the spectrum can be described as closure of an inverse orbit of a quadratic polynomial (thus having the Julia set of the quadratic polynomial as the set of accumulation points). Time permitting, relations to iterated monodromy groups will be indicated.