Stability in mirror symmetry
April 25 to April 29, 2022
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 derived categories, to symplectic geometry and
nonlinear partial differential equations.
The central topics for the
- Singularity formation in the Lagrangian Mean
Curvature Flow, and connections with J-holomorphic curves and the Fukaya
- The deformed Hermitian-Yang-Mills equation and
connections to stability conditions on the derived category of coherent
- The Thomas-Yau conjecture for Landau-Ginzburg models.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.