Asymptotics and Spectra of Cayley and Schreier Graphs of Branch Groups

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.