Selfsimilar groups and conformal dynamics

This workshop, sponsored by AIM and the NSF, 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.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email workshops@aimath.org

Plain text announcement or brief announcement.

Go to the American Institute of Mathematics.
Return to the AIM Research Conference Center.