Its–Lisovyy–Prokhorov conjecture on the monodromy symplectic form

Let $A_j$ and $G_j$ be the residue and diagonalizing data of the Fuchsian system, let $t_j$ be its pole positions, and let $\mathcal M$ be the monodromy manifold. Define the 1-form

$$\Theta_{ILP}=\sum_{j<k}^N\operatorname{tr}(A_jA_k)\,\mathrm d\log(t_j-t_k)+\sum_{j=1}^N\operatorname{tr}(L_jG_j^{-1}\,\mathrm d_{\mathcal M}G_j).$$

Here $\mathrm d_{\mathcal M}$ denotes differentiation with respect to monodromy data. Its–Lisovyy–Prokhorov conjecture. The form $\mathrm d\Theta_{ILP}$ coincides with the natural symplectic form on the monodromy manifold. This conjecture identifies the closed 2-form arising from the Malgrange-type 1-form with the natural symplectic structure on monodromy data; the supplied text does not state whether it has been proved or disproved.