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## 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

This workshop, sponsored by AIM and the NSF, 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 long-standing 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.

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.

Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than May 1, 2023. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.

Before submitting an application, please read the description of the AIM style of workshop.