5 problems

Let the $u$-plane be the modular curve parametrizing the vacua of the low-energy effective theory, and let the regularized $u$-plane integral have boundary contributions from the c…

Let $\mathcal{F}$ be a generic holomorphic foliation on the complex projective plane $\mathbb{CP}^2$. A leaf of $\mathcal{F}$ is a Riemann surface, and a topological cylinder is a…

Let $S$ be a closed, oriented surface smoothly embedded in $\mathbb{C}\mathbb{P}^2$. Write $d_a(S)$ for its algebraic degree and $g(S)$ for its genus. Topologically locally-flat Th…

Let $n\leq 8$ and let ${\mathbf c}=c_1\geq\cdots\geq c_n>0$ be admissible capacities. Write $\Im\!\operatorname{Emb}_n({\mathbf c},{\mathbf C}{\mathbf P}^2)$ for the space of sympl…

Torre's conjecture. Any monotone Lagrangian torus in $\mathbb{C}P^2$ is of the form $T(a^2,b^2,c^2)$, up to symplectomorphism.