4 problems

Let $W^1(\bar\partial_0,\Phi_0)$ be one of the Lagrangians arising from the conformal-limit construction, and let $M_{dR}$ be the de Rham moduli space. Simpson's conjecture. The La…

Let $C$ be a compact connected Riemann surface, let $D$ be an effective divisor on $C$, and let $M_H$ and $M_{dR}$ denote the relevant Higgs and de Rham moduli spaces. Let…

Let $\Sigma$ be a compact Riemann surface of genus $g>1$, let $E$ be a complex vector bundle of rank $n$ and degree zero, and let $M_{dR}$ be the de Rham moduli space of complex fl…

Simpson's conjecture. For every stable fixed point $[(\overline\partial_0,\Phi_0)]\in M_H^{\mathbb C^{\star}}$, the holomorphic Lagrangian $W^1(\overline\partial_0,\Phi_0)$ is clos…