1. Lagrangian Mean Curvature Flow

Uniqueness of JoyceLeeTsui translator
Problem 1.05.
Let $L_t$ be an ancient, almost calibrated, connected, exact LMCF. Assume that the tangent flow at $\infty$ is equal to $P_1\cup P_2$ where $P_1, P_2$ are two Lagrangian planes in $\mathbb{C}^2$ meeting along a line. Must $L_t$ be the JoyceLeeTsui translator or $P_1\cup P_2$? (What if we assume that $L_t$ is a translator?) 
Weak LMCF
Brakke flow is not a good notion of a weak solution in the Lagrangian setting because it does not preserve the Lagrangian condition through singularities.Problem 1.1.
Find a good notion of weak solutions to LMCF. 
Examples of noncompact Special Lagrangians
Problem 1.15.
Find new examples of noncompact Special Lagrangians. (For example in $T^{\star}S^n$) 
Generic singularities of LMCF
Problem 1.2.
Is the Lawlor neck a generic singularity for LMCF? 
Singularities of LMCF
Problem 1.25.
Can we classify the singularities of LMCF in the equivariant setting? 
Lagrangians in LandauGinzburg models
Problem 1.3.
Are there good conditions for the existence of calibrated Lagrangians in LandauGinzburg models? 
Characterize Translators for LMCF
Problem 1.35.
Under what conditions will eternal solutions to LMCF be translators? 
Characterize flat Lagrangian shrinkers
Problem 1.4.
Under what conditions must a noncompact complete Lagrangian shrinker be flat? (e.g. is one end and simply connected enough?) 
Classification of Lagrangian tori
Problem 1.45.
Can we classify Lagrangian shrinking tori in $\mathbb{C}^2$? 
Blowup of mean curvature at type II singularity
Problem 1.5.
Does the mean curvature blowup at a type II singularity? (Construct examples where it does not.) 
Preserving HS conditions
Problem 1.55.
Can we somehow couple the LMCF to the KählerRicci flow to preserve the Hamiltonian stationary condition? 
LMCF and holomorphic curves
Problem 1.6.
Relate the behaviour of LMCF to the existence of Jholomorphic curves. 
Convergence of LMCF
Problem 1.65.
Does the LMCF converge if the length of the path in the space of calibrated Lagrangian remains bounded?
Cite this as: AimPL: Stability in mirror symmetry, available at http://aimpl.org/stabmirrorv.