7 problems

Let the parameter space of hyperbolic monopoles contain a compact subset and a disjoint subset, and let the monopoles have sufficiently small mass. Small-mass asymptotic separation…

Let $\omega$ be the symmetric measure on the sphere at infinity $S^2$ of hyperbolic space ${\mathbb H}^3$. For $f\in C^0_c({\mathbb H}^3)$, define the action … where $x$ is regarde…

Charge-existence conjecture. For a given $\mu$ there are monopoles with any collection of nonnegative magnetic charges $(m_1,\ldots,m_s)$. Given a choice of magnetic charges, there…

Let $G_c$ be the compact form of a gauge group, and let $mu$ and $\lambda$ be coweights with $\lambda$ dominant. For dominant $nu$ satisfying $mu\leqnu\leqlambda$, let…

Sen's conjecture. If $k$ and $\ell$ are coprime, then

Theta-function vanishing conjecture. For each such pair $(m,n)$, $H(y)$ vanishes $2(|n|-1)$ times on the interval $\lambda\in(0,2)$.

Uniqueness conjecture. For a symmetric monopole, the denominator of $Q_0(z)$ has $2(|n_1|-1)$ zeros, and consequently the tetrahedrally symmetric monopole is the only monopole in t…