for this workshop
Discrete and combinatorial homotopy theory
American Institute of Mathematics, San Jose, California
Helene Barcelo, Antonio Rieser, and Volkmar Welker
This workshop, sponsored by AIM and the NSF, will be devoted to homotopy theories developed for the study of discrete and combinatorial objects. Many different models of discrete homotopy have emerged in the past 20-30 years, developed largely in isolation from one another. In this workshop, we will study different perspectives on discrete homotopy and explore their connections and differences. Among our goals is to identify important applications, particularly to combinatorics, metric geometry, and geometric group theory. We will also investigate how ideas from abstract homotopy theory (model categories, simplicial and cubical homotopy, infinity categories, etc.) may be used to extend and consolidate the theories.
The main topics of this workshop are:
- A-theory of graphs and simplicial complexes
- Homotopy of digraphs
- Digital homotopy
- Discrete homotopy of metric spaces
- Homotopy theory in topological categories
- Applications of abstract homotopy theory to discrete homotopy
- Applications of discrete homotopy to combinatorics, metric geometry, geometric group theory, and other areas.
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 December 1, 2022. 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.
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