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

Original Announcement

This workshop 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.‚Äč

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Workshop Videos