3 problems

Collie–Tong conjecture on Chern–Simons vortex dynamics
arXiv@arxiv
Collie–Tong conjecture. Chern–Simons vortex dynamics is controlled by RMG motion in $M_n$ in the small $\kappa$ (and small energy) limit.
Problemopenchern-simons-vortices ricci-magnetic-geodesics vortex-dynamics
0
RMG completeness implies geodesic completeness
arXiv@arxiv
RMG completeness conjecture. If $M$ is RMG complete, then it is geodesically complete.
Conjectureopengeodesic-completeness kahler-geometry ricci-magnetic-geodesics
0
RMG completeness conjecture for rational-map moduli spaces
arXiv@arxiv
RMG completeness conjecture. ${\sf Rat}_n$ is RMG complete for all $n\geq 2$ , despite being geodesically incomplete.
Conjectureopenmoduli-spaces rational-maps ricci-magnetic-geodesics
0

Collie–Tong conjecture on Chern–Simons vortex dynamics