for this workshop
Uniform Roe algebras: structure and invariants
at the
American Institute of Mathematics, Pasadena, California
organized by
Bruno de Mendonca Braga, Ilijas Farah, Alessandro Vignati, and Rufus Willett
This workshop, sponsored by AIM and the NSF, will be devoted to studying the structure and invariants of $C^*$-algebras of bounded operators which encode the large-scale geometry of metric or, more generally, coarse spaces. In particular, uniform Roe algebras and quasi-local algebras will be at the center of the workshop.
In view of recent breakthroughs — including Ozawa’s result on the difference between quasi-local and uniform Roe algebras and new coarse rigidity results — the workshop aims to tackle several pressing open problems. Despite these recent advances, pinning down the precise difference between these two algebras remains an open challenge, particularly in understanding when a quasi-local algebra contains a Cartan subalgebra. Rigidity questions also remain open outside the metrizable world, and, even for metrizable spaces, the relation between the homology and K-theory of these algebras is still poorly understood. Participants will also examine the ideal structures of these algebras via inverse semigroup actions. By uniting perspectives from $C^*$-dynamics, geometry, and logic, the workshop will establish a collaborative framework to resolve these interconnected questions.
Topics:
- Consequences of rigidity for the relationship between K-theory of (uniform) Roe algebras, and uniformly finite homology.
- Study of ghost operators and their relation to masas and ideals in quasi-local and uniform Roe algebras.
- Study of dynamics in large scale geometry and its relation with uniform Roe algebras and their ideal structure.
- Study of the relationship between quasi-local and uniform Roe algebras.
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 November 1, 2026.
Before submitting an application, please read the description of the AIM style of workshop.
For more information email workshops@aimath.org
