for this workshop

## Random walks beyond hyperbolic groups

at the

American Institute of Mathematics, San Jose, California

organized by

Joseph Maher, Yulan Qing, and Giulio Tiozzo

This workshop, sponsored by AIM and the NSF, will be devoted to extending results on random walks known for Lie groups or hyperbolic groups, to the more general class of groups which have actions on (non-proper) Gromov hyperbolic spaces.

There is a well-developed theory of random walks on word hyperbolic groups, extending the original development of random walks on Lie groups and their discrete subgroups. Recently, there has been much work in geometric group theory studying larger classes of groups which need not be hyperbolic, but act on (non-proper) hyperbolic spaces. Examples include relatively hyperbolic groups, acylindrical groups, WPD groups and weakly hyperbolic groups.

The goal of this workshop is to bring together people with expertise in geometric group theory, ergodic theory, probability and related areas to develop the theory of random walks on groups of isometries of hyperbolic spaces and other metric spaces, addressing several open problems.

The main topics for the workshop are:

- Central and local limit theorems
- Green metrics and Poisson Boundaries
- Locally compact groups and the Cremona group

This event will be run as an AIM-style workshop. 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*