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Explore extremal Lagrangian tori in toric domains through this advanced mathematics lecture from the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar. Delve into the concept of symplectic area of Lagrangian submanifolds, defined as the minimal positive symplectic area of a smooth 2-disk with boundary on the submanifold. Learn about extremal Lagrangian tori, which are those that maximize symplectic area among all Lagrangian tori in a given space. Discover the key result that every extremal Lagrangian torus in the standard symplectic unit ball is entirely contained in the boundary of the ball, confirming a conjecture by Cieliebak and Mohnke. Gain insights into cutting-edge research in symplectic geometry and understand the geometric implications of this boundary containment property for extremal tori.
