Geometry and topology of Artin groups
September 11 to September 15, 2023
at the
American Institute of Mathematics,
Pasadena, California
organized by
Ruth Charney,
Kasia Jankiewicz,
and Kevin Schreve
Original Announcement
This workshop will be devoted to the study of geometric and topological aspects of Artin groups. Artin groups form a rich and mysterious class of groups, and can be thought of as a (vast) generalization of braid groups. They are a large source of important examples in geometric group theory, and have been studied using tools from various areas, including combinatorics, geometric topology, and nonpositively curved geometry. There has been an enormous amount of progress in the field in the past couple of years. We believe that bringing together experts on various aspects of Artin groups will lead to new approaches to resolving some of the longstanding questions.
The main topics for the workshop are:

The $K(\pi,1)$conjecture, in particular the dual approach using Garside structures which led to a recent breakthrough in the case of affine Artin groups.

Nonpositively curved aspects of Artin groups, in particular the existence of CAT(0) structures, actions on Helly spaces and systolic complexes, and acylindrical hyperbolicity.

Subgroup structure of Artin groups, for example the Tits Alternative, Wise’s power alternative, and the generalized Tits Conjecture.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.