6 problems

Let $\Sigma_0$ and $\Sigma_1$ be homotopy spheres, and let $\Sigma_0\subset T^*\Sigma_1$ be a Lagrangian embedding. A bundle of rigid tubes over $\Sigma_1$ is a tube bundle of the…

For $a\ge1$, define the embedding capacity … Here $E^4(1,a)$ and $B^k(r)$ are the standard symplectic ellipsoid and ball, respectively. The Lagrangian embedding capacity identity.…

Let $N$ and $L$ be closed, simply connected manifolds of the same dimension. The cotangent bundle $T^*N$ carries its natural symplectic structure, and consider the space of Lagrang…

Let $(\mathbb{R}^4,\omega_{std})$ be standard symplectic four-space, and allow Lagrangian surfaces to have open Whitney umbrella singularities. An exact Lagrangian surface is a Lag…

Let $\mathbb{K}^2$ denote the Klein bottle. A Lagrangian embedding is an embedding whose image is a Lagrangian submanifold of $(\mathbb{C}^2,\omega_{std})$. Givental's conjecture.…

Let $L$ and $N$ be simply connected manifolds, and let $ST^*L$ denote the unit cotangent sphere bundle of $L$, viewed as a contact manifold embedded in $T^*N$. An exact Lagrangian…