5 problems

Kerz's commutativity conjecture. (i) For any $\lambda\in\mathbb R^*$, $\lambda\cdot\sigma_{\operatorname{Dol}}$ is also an isomonodromic deformation. (ii) For any…

Let $\mathcal T_g$ denote the Teichmüller space of compact Riemann surfaces of genus $g\geq2$, let $\mathcal X/\mathcal T_g$ be its universal family, and let…

Let $\mathcal T_g$ be the Teichmüller space of genus $g\geq 2$ compact Riemann surfaces, with universal family $\mathcal X/\mathcal T_g$. For an isomonodromic section…

Jimbo–Miwa–Ueno differential conjecture. One has

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…