4 problems

Asymptotic expansion conjecture. The asymptotic expansion of $\operatorname{Tr} f(s,s;\mathbf{x})$ is determined to all orders by the conserved quantities…

Large-charge Nahm-data convergence conjecture. For each solution $(t^i)$ corresponding to a magnetic bag, there is a sequence of solutions $(T^i_{(n)})$ such that, as…

Bolognesi's conjecture. For any magnetic bag $(f,\phi)$, there is a sequence $(A^{(n)},\Phi^{(n)})$ of charge-$n$ solutions such that, as $n\rightarrow\infty$,

The Nahm equations provide the data for the ADHMN construction of BPS monopoles, whose Weyl equation yields the Higgs field and gauge potential through normalized solutions. In the…