Applications are closed
for this workshop

Stability in mirror symmetry

April 25 to April 29, 2022

at the

American Institute of Mathematics, San Jose, California

organized by

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 derived categories, to symplectic geometry and nonlinear partial differential equations.

The central topics for the workshop are:

  1. Singularity formation in the Lagrangian Mean Curvature Flow, and connections with J-holomorphic curves and the Fukaya category.

  2. The deformed Hermitian-Yang-Mills equation and connections to stability conditions on the derived category of coherent sheaves.

  3. The Thomas-Yau conjecture for 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.

The deadline to apply for support to participate in this workshop has passed.

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