IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

The symplectic area of a Lagrangian submanifold L in a symplectic manifold is defined as the minimal positive symplectic area of a smooth 2-disk with boundary on L. A Lagrangian torus is called extremal if it maximizes the symplectic area among all Lagrangian tori. I will explain that every extremal Lagrangian torus in the standard symplectic unit ball is entirely contained in the boundary of the ball. This result confirms a conjecture of Cieliebak and Mohnke in the affirmative. (Ref: arXiv:2504.13076)