#
Selfsimilar groups and conformal dynamics

June 5 to June 9, 2006
at the

American Institute of Mathematics,
Palo Alto, California

organized by

Rostislav Grigorchuk and Kevin Pilgrim

## Original Announcement

This workshop will be devoted to developing
newly discovered connections between the theory of automaton groups and
conformal dynamical systems. On the one hand, conformal dynamical systems
yield a rich source of such groups with interesting algebraic, geometric, and
spectral properties. On the other hand, such groups can be shown to yield
conformal dynamical systems with remarkable geometric and measure-theoretic
regularity. This connection is established by means of the theory of Gromov
hyperbolic spaces. Partial results suggest a deep relationship between
algebraic properties of groups and geometric properties of dynamical systems.
Initial lectures will be devoted to the algebraic properties of automaton and
iterated monodromy groups, the theory of Gromov hyperbolic spaces, and how
together these combine to yield abstract models which are conformal dynamical
systems. These lectures will be accessible to a general mathematical audience.
Topics will then focus on explaining and developing relationships between
algebraic and geometric properties.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

A continually revised
survey article
on Selfsimilar groups and conformal dynamics
is being put together by Kevin Pilgrim.