8 problems

For each integer $m\geq 2$, let $(Y_m,\omega_m)$ be the toric symplectic manifold obtained from $\mathbb{CP}^{2}$ with lines of area $m+2$ by symplectically blowing up along the st…

Let $d4c$ be a Plücker sequence of type $(k,n)$, and let $L_\mathfrak{s}\subset\operatorname{Gr}(k,n)$ be its associated Plücker torus. The Laurent polynomial $W_\mathfrak{s}$ is d…

For each Markov triple $(a,b,c)\in\mathfrak M$, let $T_{a,b,c}\subset\mathbb{C}P^2$ be Vianna's monotone Lagrangian torus, and let ${\frak w}_{\text{DW}}(T_{a,b,c};\mathbb{C}P^2)$…

Let $T_{a,b,c}\subset\mathbb{C}P^2$ be Vianna's torus associated with a Markov triple $(a,b,c)$, let $\mathbb{R}P^2\subset\mathbb{C}P^2$ be the real projective plane, and let…

Let $T_{a,b,c}\subset \mathbb{C}P^2$ be Vianna's monotone Lagrangian torus associated with a Markov triple $(a,b,c)\in\mathfrak M$. A capacity conjecture. There is no monotone symp…

Let $\mathbb{C}P^n$ carry the Fubini–Study symplectic form $\omega_{\operatorname{FS}}$. A Lagrangian torus $L\subset \mathbb{C}P^n$ is extremal when it realizes the relevant Lagra…

Let $D^{2n}$ be the $2n$-dimensional unit disc with the standard symplectic form $\omega0$, and let $S^{2n-1}=\partial D^{2n}$. A Lagrangian torus $Lsubset D^{2n}$ is extremal w…

Let $T^c_{r,0}$ be a Lagrangian torus in $\mathbb{CP}^1\times\mathbb{CP}^1$ of type $T(1,2,9)$, and let a family of Maslov-index-$2$ holomorphic discs mean a family of such discs w…