4 problems

Let $h_a$ denote the bifurcation field for asymmetric solutions and $h_s$ the bifurcation field for symmetric solutions, and consider parameters $(\kappa,d)$ for which asymmetric s…

Aftalion's conjecture. Asymmetric solutions can have lower energy than the symmetric solutions.

Marcus's conjecture. A minimizer of $\mathcal G$ is probably a symmetric solution satisfying (1.2)–(1.6). The source leaves open whether asymmetric solutions may also exist as mini…

CLE(4) level-set conjecture. The level sets of the Ginzburg–Landau model with zero boundary condition should converge to CLE(4).