for this workshop
Stability in mirror symmetry
American Institute of Mathematics, San Jose, California
Tristan C. Collins and Jason D. Lotay
This workshop, sponsored by AIM and the NSF, will bring together mathematicians from a variety of backgrounds to discuss a central problem in mirror symmetry: the existence of special Lagrangian submanifolds, and their holomorphic mirrors, stable vector bundles. These two classes of objects form a set of canonical geometric objects, described by fully nonlinear partial differential equations (PDEs), which play a central role in mirror symmetry. Dating back to work of Thomas-Yau, it has long been conjectured that the existence of solutions to these nonlinear PDEs is equivalent to a purely algebraic notion of stability. This conjectural picture connects diverse fields of mathematics, ranging from stability conditions on derived categories, to symplectic geometry and the Fukaya category, to the study of the Lagrangian mean curvature flow and fully nonlinear systems of PDEs.
The central topics for the workshop are:
- The Lagrangian Mean Curvature Flow, singularity analysis, and connections with the Fukaya category.
- The deformed Hermitian-Yang-Mills equation, infinite dimensional GIT, and fully nonlinear systems.
- Understanding the Thomas-Yau conjecture for toric Fano manifolds and Landau-Ginzburg models.
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 June 7, 2020. 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 firstname.lastname@example.org