for this workshop
Wall-crossing: techniques and applications
at the
American Institute of Mathematics, Pasadena, California
organized by
Nikolas Kuhn, Henry Liu, and Felix Thimm
This workshop, sponsored by AIM and the NSF, will be devoted to new developments in wall-crossing for enumerative invariants of abelian categories, with a focus on identifying promising applications.
Specifically, Joyce’s recent "universal" wall-crossing formalism provides a way to systematically study wall-crossing phenomena for a reasonably large class of linear categories. It generalizes previous wall-crossing formalisms of Joyce-Song and Kontsevich-Soibelman, which are controlled by Hall algebras. Strategies that have been successful there may now be applied to new enumerative settings: moduli spaces of sheaves on surfaces, Calabi-Yau 3-folds and 4-folds; for equivariant and/or K-theoretic refinements of ordinary enumerative invariants; etc. Remarkably, the new wall-crossing formula is controlled by a vertex algebra, constructed naturally and geometrically from the moduli stack, indicating new and fruitful interactions with the theory of vertex algebras.
We plan to bring together experts from enumerative geometry, mathematical physics and geometric representation theory to explore connections between these fields through the lens of these new developments.
The main topics for the workshop are:
- Applications to sheaf-counting invariants, e.g. Vafa-Witten theory
- Vertex algebras, Hall algebras, and their representation theories
- Structures in enumerative invariants: modularity, resurgence, etc.
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, 2025.
Before submitting an application, please read the description of the AIM style of workshop.
For more information email workshops@aimath.org
