Stability in mirror symmetry
December 7 to December 11, 2020
American Institute of Mathematics,
San Jose, California
Tristan C. Collins and Jason D. Lotay
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 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.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
Papers arising from the workshop: