| Abstract: |
| We define a shape invariant, a sort of set valued symplectic capacity, for domains in $\mathbb{R}^4$. The shape of a domain $X$ captures the Hamiltonian isotopy classes, in $\mathbb{R}^4$, of embedded Lagrangian tori in $X$. Then we describe computations for a class of toric $X$, showing that the moment image and the shape coincide in certain regions. Hence we have rigidity for many symplectic embedding problems. This reports on joint work with Ely Kerman and Jun Zhang. |
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