3 problems

Gravitating coupled vortex conjecture. The pair $(\mathbb{P}^1,T)$ admits a solution to the gravitating coupled vortex equations if and only if $T$ is $\sigma$-polystable and the p…

Let $X=\mathbb{R}^3\cup\{\infty\}$ and let $U:X\to S^3$ be a map of degree $B$. Interpret $U$ as two vortices in $\psi_1$ and $\psi_2$ of $\boldsymbol{\psi}\in S^3$, with winding n…

Let $H$ be the Hamiltonian in the paper's equation (Hamiltonian), and let $\widetilde{H}$ be its extended Hamiltonian in equation (HamiltonianExtended). A ladder may be closed or o…