2 problems

Joyce's classification conjecture. The cone on the Clifford torus, and perhaps also the cone $T_{1,2}$, are the only rigid special Lagrangian $T^2$-cones.

Quadratic growth conjecture. The quantities $\operatorname{l-ind}(\Sigma)$, $\operatorname{s-ind}(\Sigma)$ and $\operatorname{Area}(\Sigma)$ grow quadratically with $d$.