9 problems

Liouville conjecture. The function $f$ is constant. Equivalently, a compact generalized Calabi–Yau manifold has no nonconstant nowhere-zero smooth rescaling of a global closed gene…

Let $X$ be a generalized complex manifold, let $T_X^*\to X$ be its Poisson Lie algebroid, and let $\mathcal{X}=[X/T_X^*]$ be the corresponding quotient stack. The stack…

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.

In generalized Kähler geometry, let a generalized Kähler manifold consist of two commuting generalized complex structures $\mathbb{J}_1$ and $\mathbb{J}_2$, with $\mathbb{J}_2$ pla…

Canonical $L_{\infty}$ morphism conjecture. There is a canonical $L_{\infty}$ morphism from $\Omega^{\bullet}_{\mathbb J,H}$ to the total complex of, extending the given quasi-isom…

Mirror quantum cohomology conjecture. Variations of Hodge structure are related to a quantum cohomology ring on a mirror generalized Calabi–Yau manifold.

Let $\mathfrak g$ be a split semisimple real Lie algebra and let $e\in\mathfrak g$ be nilpotent. Denote by $P(\mathfrak g,e)$ the statement that, whenever…

Let $\mathfrak g$ be a split semisimple real Lie algebra, and let $e\in\mathfrak g$ be nilpotent. A generalized complex structure on the corresponding real nilpotent orbit is a $B$…