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.