for this workshop
Interactions between discrete and large topological groups
at the
American Institute of Mathematics, Pasadena, California
organized by
Maksym Chaudkhari, Kate Juschenko, and Friedrich Martin Schneider
This workshop, sponsored by AIM and the NSF, is aimed at developing connections between dynamics of large topological groups on the one hand and combinatorics of their countable discrete subgroups on the other. Particular focus will be on amenability and amenability-like properties (for instance, extreme amenability, Liouville property, skew-amenability, extensive amenability, etc.). One of the main objectives of the workshop is to put substantial effort into attacking several problems in group theory by connecting researchers in several fields.
The main topics for the workshop are:
- connections between amenability-like properties of transformation groups, such as automorphism groups of discrete structures, and combinatorial properties of the objects on which they act;
- the interplay between measured group theory, topological dynamics and analysis, for instance in the study of full groups of measured equivalence relations or their $L^1$ counterparts, and their potential applications to asymptotic properties of discrete groups;
- realizations of countable groups as dense or discrete subgroups of large topological groups;
- approaches to amenability of the groups of dynamical origin, such as Thompson’s group $F$ or the group of interval exchange transformations, via concrete actions and their properties.
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 March 4, 2025. 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.
For more information email workshops@aimath.org
