[Binghamton Geometry/Topology Seminar] (no subject)

[Ross Geoghegan]

                   BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR


   Date: Tuesday  March 28  (NOTE UNUSUAL DAY - T U E S D A Y) 

   Time:  2.50 pm

   Place: Library North 2205 followed by coffee/tea in the Anderson
          Reading Room.

   Speaker: Zoran Sunik (Texas A&M) 

   Title: Hanoi Towers, Schreier Graphs, Iterated Monodromy Groups and
          Julia sets

Abstract: 
We model the well known Hanoi Towers Problem on k pegs by a self-similar
group H(k) acting on a k-regular rooted tree. The Schreier graph of
the action of the group H(k) on level n in the tree models the n-disk
version of the problem. As n goes to infinity the obtained limiting
graph is the Schreier graph of the action of H(k) on the boundary of
the k-ary tree. For the original version of Hanoi Towers on 3 pegs the
obtained group H(3) is an automaton group branching regularly over its
commutator. The corresponding finite Schreier graphs are 3-regular graphs
that approximate the Sierpinski gasket. The group H(3) can be described
as the iterated monodromy group of a post-critically finite map f on
the Riemann sphere. The Julia set of the map f is homeomorphic to the
limiting infinite Schreier graph. The action of H(3) on the levels of
the tree provides permutational representations that can be used to
determine the spectrum of the Markov operator on the associated Schreier
graphs. The spectrum can be described as the closure of the backward
orbit of a quadratic polynomial p. It consists of a countable set of
isolated points that accumulate to a Cantor set, which is the Julia set
of the polynomial p.


NOTE: The seminar has a webpage where the semester's program is listed:

http://math.binghamton.edu/MATH/dept/topsem/index.html

It can also be linked from the Department's Home Page.
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