[Binghamton Geometry/Topology Seminar] September 17

[Marco Varisco]

Binghamton Geometry/Topology Seminar
http://www.math.binghamton.edu/dept/topsem/

Date: Thursday, September 17, 2009

Time: 2:50 pm

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

Speaker: Dmytro Savchuk

Title: Self-similar groups (or groups generated by automata) and their
connection to the holomorphic dynamics via iterated monodromy groups

Abstract: In the first talk I will introduce the notions of
self-similar groups, explain their basic properties, give examples,
motivate interest in them, and formulate several open questions. One
particular application I am going to concentrate on is a relatively
recent discovery (mainly by Nekrashevych) of the beautiful connection
between self-similar groups and holomorphic dynamics realized by
iterated monodromy groups. Here is a rough idea: with every (nice)
d-fold self-covering of a (nice) topological space X one can associate
the group acting on the tree of the preimages of any point in X by
automorphisms. It can be shown that under certain labeling of the tree
this group is self-similar. This may provide some information on the
self-covering itself. More details will be provided on the talk.