3 problems

Let $(E,\phi)$ be a Higgs bundle, let $\sigma$ be its non-abelian Hodge correspondence, and let $(\mathcal E,\Phi)$ be the singular Higgs bundle obtained from the Fourier–Mukai con…

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…

Smoothness and symplecticity conjecture. Let $\kappa\in H$. For $\nu>0$, the derived structure on ${}_{\kappa}\mathcal{M}^{0}_{\operatorname{Bet},\psi}$ is trivial, and…