The Lagrangian capacity of symplectic manifolds

par Shah Faisal (IRMA, Strasbourg)

vendredi 26 sept. 2025, 11:15 → 12:15 Europe/Paris

112 (ICJ)

A symplectic capacity is a function that assigns to each symplectic manifold a nonnegative number, which roughly measures its “symplectic size” and is invariant under symplectomorphisms (sympletic equivalence).  An important example is the Lagrangian capacity: for a Lagrangian submanifold $L$ in a symplectic manifold, the minimal symplectic area of $L$ is defined as the smallest positive symplectic area of a smooth $2$-disk with boundary on $L$.  The Lagrangian capacity of the symplectic manifold is then the supremum of these minimal areas taken over all embedded Lagrangian tori.

In this talk, I will describe problems related to the Lagrangian capacity and present some of our recent progress on this topic.