Let $(M, \omega)$ be a complex $n$-dimensional Hermitian symmetric space of compact type, where $\omega$ is the symplectic (Kaehler) form on $M$ normalized so that $[\omega]$ generates the integral cohomology class $H^2(M, Z)$. Let $A$ be the generator of $H_2(M, Z)$.

Problem: Find two submanifolds $X$ and $Y$ of $M$ such that: $$\dim_{\R} X+\dim_{\R} Y=4n-2c_1(TM)(A)$$ and $$\Phi_A([X], [Y], [p])\neq 0,$$ where $\Phi_A([X], [Y], [p])$ is the genus-zero Gromov--Witten invariant of the triple $[p], [X], [Y]$ and $[p]$, $[X]$ and $[Y]$ denote the homology classes of a point $p\in M$, $X$ and $Y$ respectively.)