5 problems

Let $X$ be a complex manifold, let $D\subset X$ be a divisor, and let $\mathcal{M}$ be a meromorphic connection on $X$ along $D$. A ramification is a finite covering adapted to a n…

Let $n$ be an even integer. An elementary wild character variety is a wild character variety arising from an elementary connection, considered up to isomorphism. Finiteness conject…

Irregular Riemann–Hilbert isomorphism conjecture. For any reductive $G$ over $\mathbb{C}$ and homogeneous element $\psi$ in $\mathfrak{g}((t))$ of slope $\nu>0$, and any…

Irregular local-system realization conjecture. The Lagrangian $L_{\cM}$ defines an object of $\Fuk_m(T^*X)$ independent of the choice of $f$. The full subcategory of $\Fuk_m(T^*X)$…

The extended Riemann–Hilbert correspondence. The map $RH$ is a Poisson isomorphism. This conjecture proposes that the decorated moduli space of irregular connections and the corres…