# Boundaries of groups

October 10 to October 14, 2016

at the

American Institute of Mathematics, San Jose, California

organized by

Jean-Francois Lafont and Genevieve Walsh

## Original Announcement

This workshop will focus on understanding boundaries of groups. These compactifications of infinite groups arise in many different ways, and can exhibit different types of structure. Moreover, these boundaries often encode various algebraic and geometric properties of the underlying group. The study of these boundaries form a central theme in modern geometric group theory.

The main topics of the workshop are:

• examples of boundaries for various classes of groups and spaces (relatively hyperbolic groups, CAT(0) groups, Fuchsian buildings, Artin groups, Coxeter groups, etc.), and comparing different boundaries for the same group.
• additional structure present on these boundaries (topological, dynamical, and/or analytic).
• applications of boundaries, particularly their use in establishing results about groups, or about spaces on which the group acts geometrically.

## Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Quasi-Mobius Homeomorphisms of Morse boundaries
by  Ruth Charney, Matthew Cordes, and Devin Murray
A rank-one CAT(0) group is determined by its Morse boundary
by  Ruth Charney and Devin Murray
On groups with $S^2$ Bowditch boundary
by  Been Tshishiku and Genevieve Walsh