2 problems

Classification conjecture. A real flag manifold $\mathbb{F}_\Theta=K/K_\Theta$ admits a $K$-invariant generalized complex structure if and only if it is of type $C_l$ and

Integrability conjecture. No maximal real flag manifold of type $C_4$ or $D_4$ admits integrable $K$-invariant generalized almost complex structures.