6 problems

Let $M$ be a Riemann surface of genus $g>1$, and let $M_N$ denote the moduli space of $N$ vortices on $M$. Its volume is defined by … where $\omega$ is the symplectic form on $M_N$…

Coupled-vortex F-term conjecture. A condition generalizing the previously defined spiked moment-map conditions is

Coupled-vortex D-term conjecture. The D-term condition and quotient are

Vortex moduli space conjecture. The space $\mathcal V_{N,p}$ is the moduli space of $N$ vortices in a $U(p)$ gauge theory.

Positivity conjecture. This behaviour should continue to hold in the interior of the moduli space, where the large-separation approximation breaks down; in particular, the scalar c…

Let $\Sigma$ be a Riemann surface, let $n>1$, and let $\mathcal M^o$ be the vortex moduli space identified with the space $\mathcal H$ of holomorphic maps…